Skip to main content

An Appreciation of James Serrin

  • Chapter
  • 257 Accesses

Abstract

I am particularly happy to have the opportunity of these proceedings to write a profile of one of my distinguished teachers, with whom I have also had the good fortune to collaborate for so many years, Professor James Serrin. Before entering into my recollection of these years of close association, I would first desire to mention the tribute that Professor Clifford Truesdell wrote in the volume of papers, Analysis and Continuum Mechanics, dedicated to James Serrin on the occasion of his sixtieth birthday, published by Springer-Verlag, in gratitude for his many years of work as coeditor of the Archive for Rational Mechanics and Analysis.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

James Serrin’s publications

  1. Free boundaries and jets in the theory of cavitation (with D. Gilbarg). J. Math. and Phys., 29 (1950), 1–12.

    MathSciNet  MATH  Google Scholar 

  2. Uniqueness theorems for two free boundary problems. Amer. J. Math., 74 (1952), 492–506.

    Google Scholar 

  3. Existence theorems for some hydrodynamical free boundary problems. J. Rational Mech. Anal., 1 (1952), 1–48.

    Google Scholar 

  4. Two hydrodynamical comparison theorems. J. Rational Mech. Anal., 1 (1952), 563572.

    Google Scholar 

  5. Notes on hydrodynamics. Photoprinted by Princeton University, 1952, 218 pages.

    Google Scholar 

  6. On plane and axially symmetric free boundary problems. J. Rational Mech. Anal., 2 (1953), 563–575.

    Google Scholar 

  7. A note on the wave equation. Proc. Amen Math. Soc., 5 (1954), 307–308.

    Google Scholar 

  8. Comparison theorem for subsonic flows. J. Math. and Physics, 23 (1954), 27–45.

    Google Scholar 

  9. On the Phragmen-Lindelőf theorem for elliptic partial differential equations. J. Rational Mech. Anal., 3 (1954), 395–413.

    Google Scholar 

  10. A uniqueness theorem for the parabolic equation u t = a(x)u xx + b(x)u x + c(x)u, Bull. Amer. Math. Soc.,60 (1954), 344.

    Google Scholar 

  11. Uniqueness of axially symmetric subsonic flow past a finite body (with D. Gilbarg). J. Rational Mech. Anal., 4 (1955), 169–175.

    MathSciNet  MATH  Google Scholar 

  12. A characterization of regular boundary points for second-order linear differential equations. Bull. Amer. Math. Soc., 61 (1955), 224.

    Google Scholar 

  13. On the Harnack inequality for linear elliptic equations. J. Analyse Math., 4 (1956), 292–308.

    Google Scholar 

  14. On isolated singularities of solutions of second-order linear elliptic equations (with D. Gilbarg). J. Analyse Math., 4 (1956), 309–340.

    Article  MathSciNet  MATH  Google Scholar 

  15. A note on harmonic functions defined in a half-plane. Duke Math. J., 24 (1956), 523–526.

    Google Scholar 

  16. On the Wilder continuity of quasi-conformal and elliptic mappings (with R. Finn). Trans. Amer. Math. Soc., 89 (1958), 1–15.

    MathSciNet  MATH  Google Scholar 

  17. Mathematical Principles of Classical Fluid Mechanics (Monograph). Handbuch der Physik, VIII/1 (1959), pp. 125–263. Russian translation: Foreign Literature Publishing House, Moscow, 1963, 265 pages.

    Google Scholar 

  18. On the stability of viscous fluid motion. Arch. Rational Mech. Anal., 3 (1959), 1–13.

    Google Scholar 

  19. A note on the existence of periodic solutions of the Navier—Stokes equations. Arch. Rational Mech. Anal., 3 (1959), 120–122.

    Google Scholar 

  20. On the uniqueness of compressible fluid motions. Arch. Rational Mech. Anal., 3 (1959), 271–288.

    Google Scholar 

  21. On the derivation of stress-deformation relations for a Stokesian fluid. J. Math. Mech., 8 (1959), 459–470.

    Google Scholar 

  22. Poiseuille and Couette flow of non-Newtonian fluids. Z. Angli. Math. Mech., 39 (1959), 295–299.

    Google Scholar 

  23. On a fundamental theorem of the calculus of variations. Acta Math., 102 (1959), 1–22.

    Google Scholar 

  24. A new definition of the integral for non-parametric problems in the calculus of variations. Acta Math., 102 (1959), 23–32.

    Google Scholar 

  25. The exterior Dirichlet problem for second-order elliptic equations (with N. Meyers). J. Math. Mech., 9 (1960), 513–538.

    MathSciNet  MATH  Google Scholar 

  26. On the area of curved surfaces. Amer. Math. Monthly, 68 (1961), 435–140.

    Google Scholar 

  27. On the differentiability of functions of several variables. Arch. Rational Mech. Anal., 7 (1961), 359–372.

    Google Scholar 

  28. On the definition and properties of certain variational integrals. Trans. Amer. Math. Soc., 101 (1961), 139–167.

    Google Scholar 

  29. On the entropy change through a shock layer (with Y.C. Whang). J. Aerospace Sci., 28 (1961), 990–991.

    MathSciNet  MATH  Google Scholar 

  30. Dirichlet’s Principle in the Calculus of Variations. Proc. Symposia in Pure Math., vol. 4. American Mathematical Society, Providence, RI, 1961, pp. 17–22.

    Google Scholar 

  31. Interior estimates for solutions of the Navier—Stokes equations. In Partial Differential Equations and Continuum Mechanics, (R. Langer, ed. ). University of Wisconsin Press, 1961, pp. 376–378.

    Google Scholar 

  32. On the interior regularity of weak solutions of the Navier—Stokes equations. Arch. Rational Mech. Anal., 9 (1962), 187–195.

    Google Scholar 

  33. Strong convergence in a product space. Proc. Amer. Math. Soc., 13 (1962), 651–655.

    Google Scholar 

  34. The initial value problem for the Navier—Stokes equations. In Nonlinear Problems (R.E. Langer, ed. ). University of Wisconsin Press, 1963, pp. 69–98.

    Google Scholar 

  35. Variational problems of minimal surface type, I (with H. Jenkins). Arch. Rational Mech. Anal., 12 (1963), 185–212. See also entries [50], [59].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. A Harnack inequality for non-linear equations. Bull. Amer. Math. Soc., 69 (1963), 481–486.

    Google Scholar 

  37. Comparison and averaging methods in mathematical physics. In Proprietà di Media e Teoremi di Confronte in Fisica Matematica. Centro Internazionale Matematico Estivo, Rome, Edizioni Cremonese, 1965, pp. 1–87.

    Google Scholar 

  38. A priori estimates for solutions of the minimal surface equation. Arch. Rational Mech. Anal., 14 (1963), 376–383. See also entry [57].

    Google Scholar 

  39. Mathematical Aspects of Boundary Layer Theory. Notes taken by H.K. Wilson, Department of Mathematics, University of Minnesota, 1963 (131 pages, multiplied typescript).

    Google Scholar 

  40. Sublinear functions of measures and variational integrals (with C. Goffman). Duke Math. J., 31 (1964), 159–178.

    Article  MathSciNet  MATH  Google Scholar 

  41. Local behavior of solutions of quasi-linear equations. Acta Math., 111 (1964), 247–302.

    Google Scholar 

  42. H = W (with Norman Meyers). Proc. Nat. Acad. Sci., 51 (1964), 1055–1056.

    Google Scholar 

  43. Removable singularities of solutions of elliptic equations. Arch. Rational Mech. Anal., 17 (1964), 67–78. See also entry [48].

    Google Scholar 

  44. Pathological solutions of elliptic differential equations. Ann. Scuola Norm. Sup. Pisa, Sci. Fis. Math., 18 (1964), 385–387.

    Google Scholar 

  45. Singularities of Solutions of Nonlinear Equations. Proc. Symposia in Pure Math., vol. 17, pp. 68–88. American Mathematical Society, Providence, RI, 1965.

    Google Scholar 

  46. Isolated singularities of solutions of quasi-linear equations. Acta Math., 113 (1965), 219–240.

    Google Scholar 

  47. Theory of differentiation. Notes taken by T. Hatcher, Department of Mathematics, University of Minnesota, 1965 (135 pages, multiplied typescript).

    Google Scholar 

  48. Removable singularities of solutions of elliptic differential equations, II. Arch. Rational Mech. Anal., 20 (1965), 163–169.

    Google Scholar 

  49. The Dirichlet problem for the minimal surface equation with infinite data (with H. Jenkins). Bull. Amer. Math. Soc.,72 (1966), 102–106. See also entry [59].

    Article  MathSciNet  MATH  Google Scholar 

  50. Variational problems of minimal surface type, II: Boundary value problems for the minimal surface equation (with H. Jenkins). Arch. Rational Mech. Anal., 21 (1966), 321–342.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. Isolated singularities of solutions of linear elliptic equations (with H. Weinberger). Amer. J. Math., 88 (1966), 258–272.

    Article  MathSciNet  MATH  Google Scholar 

  52. Local behavior of solutions of quasi-linear parabolic equations (with D.G. Aronson). Arch. Rational Mech. Anal., 25 (1967), 81–122.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. A maximum principle for nonlinear parabolic equations (with D.G. Aronson), Ann. Scuola Norm. Sup. Pisa, Sci. Fis. Mat., 21 (1967), 291–305.

    MathSciNet  MATH  Google Scholar 

  54. The Dirichlet problem for quasi-linear elliptic equations with many independent variables. Proc. Nat. Acad. Science, 58 (1967), 1829–1835. See also entry [64].

    Google Scholar 

  55. On the asymptotic behavior of velocity profiles in the Prandtl boundary layer theory, Proc. Roy. Soc. London Set: A, 299 (1967), 491–507.

    Google Scholar 

  56. The Dirichlet problem for the minimal surface equation in higher dimensions (with H. Jenkins) J. Reine Angli. Math., 223 (1968), 170–187.

    Article  MathSciNet  Google Scholar 

  57. Addendum to: A piori estimates for solutions of the minimal surface equation. Arch. Rational Mech. Anal., 28 (1968), 149–154.

    Google Scholar 

  58. On the mathematical basis of Prandtl’s boundary layer theory: An example. Arch. Rational Mech. Anal., 28 (1968), 217–225.

    Google Scholar 

  59. Variational problems of minimal surface type, III: The Dirichlet problem with infinite data (with H. Jenkins). Arch. Rational Mech. Anal., 29 (1968), 304–322.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  60. The behavior of similar solutions in a compressible boundary layer (with J.B. McLeod). J. Fluid Mech., 34 (1968), 337–342.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  61. A new proof in differentiation theory. Notices Amen Math. Soc., 15 (1968), 1036. Abstract; see also W. Rudin, Real and Complex Analysis, 2nd edn. McGraw-Hill, New York, 1974, pp. xii, 435, and 162–167.

    Google Scholar 

  62. A general chain rule for derivatives and the change of variable formula for the Lebesgue integral (with D.E. Varberg). Amer. Math. Monthly, 76 (1969), 514–520.

    Article  MathSciNet  MATH  Google Scholar 

  63. The existence of similar solutions for some laminar boundary layer problems (with J.B. McLeod). Arch. Rational Mech. Anal., 31 (1969), 288–303.

    MathSciNet  ADS  Google Scholar 

  64. The problem of Dirichlet for quasi-linear elliptic differential equations with many independent variables. Philos. Trans. Roy. Soc. London Ser., A, 264 (1969), 413–496.

    Google Scholar 

  65. On surfaces of constant mean curvature which span a given space curve. Math. Z., 88 (1969), 77–88.

    Google Scholar 

  66. Existence theorems for some compressible boundary layer problems. In Qualitative Theory of Nonlinear Differential and Integral Equations. SIAM Stud. Appl. Math., vol. 5 1970, pp. 35–42.

    Google Scholar 

  67. The Dirichlet problem for surfaces of constant mean curvature. Proc. London Math. Soc., 21 (1970), pp. 361–384.

    Google Scholar 

  68. On the strong maximum principle for nonlinear second-order differential inequalities. J. Funct. Anal., 5 (1970), 184–193.

    Google Scholar 

  69. Boundary curvatures and the solvability of Dirichlet’s Problem. Proc. International Congress of Mathematicians (Nice, 1970), vol. 2, Paris, 1970, 867–875.

    Google Scholar 

  70. Curvature inequalities for surfaces over a disk (with H.F. Weinberger). In Some problems of Mathematics and Mechanics—M.A. Lavrentieff Anniversary Volume. Nauka Leningrad, 1970, pp. 242–250. English version: Amer. Math. Soc. Translation, vol. 104, 1976, 223–231.

    Google Scholar 

  71. Recent developments in the mathematical aspects of boundary layer theory. Internat. J. Engng. Sci., 9 (1971), 233–240.

    Google Scholar 

  72. Uniqueness and comparison theorems for nonlinear elliptic equations in divergence form (with J. Douglas, Jr. and T. Dupont). Arch. Rational Mech. Anal., 42 (1971), 157–168.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  73. A symmetry problem in potential theory. Arch. Rational Mech. Anal., 43 (1971), 304–318.

    Google Scholar 

  74. Gradient estimates for solutions of nonlinear elliptic and parabolic equations. In Contributions to Nonlinear Functional Analysis (E. Zarantonello, ed. ). University of Wisconsin Press, 1971, 565–601.

    Google Scholar 

  75. Nonlinear elliptic equations of second order. Lectures at Symposium on Partial Differential Equations, Berkeley, 1971. Mimeographed notes (57 pages, multiplied typescript).

    Google Scholar 

  76. The swirling vortex. Philos. Trans. Roy. Soc. London Ser. A, 271 (1972), 325–360.

    Google Scholar 

  77. Entire solutions of nonlinear Poisson equations. Proc. London Math. Soc., 24 (1972), 348–366.

    Google Scholar 

  78. A note on the preceding paper of Amann. Arch. Rational Mech. Anal., 44 (1972), 182–186.

    Google Scholar 

  79. Rectilinear steady flow of simple fluids (with R.L. Fosdick). Proc. Royal Soc. London, 332 (1973), 311–333.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  80. Global properties of continuum thermodynamic processes (with R.L. Fosdick). Arch. Rational Mech. Anal., 59 (1975), 97–109.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  81. On the axioms of classical mechanics. Department of Mathematics, University of Minnesota, 1974 (74 pages, multiplied typescript).

    Google Scholar 

  82. Liouville theorems for nonlinear Poisson equations. In Convegno Internazionale sui Metodi Valutativi nella Fisica—Matematica, Accad. Naz. Lincei, Problemi Attuali di Scienza e di Cultura, vol. 217, 1975, pp. 207–215.

    Google Scholar 

  83. Doomsday: On target? Science Magazine, 189, July 11, 1975, pp. 86–87.

    Google Scholar 

  84. The solvability of boundary value problems: Hilbert’s twentieth problem. In Mathematical Developments Arising from Hilbert Problems, Proc. Sympos. Pure Math., vol. 28, American Mathematical Society, Providence, RI, 1976, pp. 507–524.

    Google Scholar 

  85. Liouville theorems and gradient bounds for quasi-linear elliptic systems. Arch. Rational Mech. Anal., 66 (1977), 295–310.

    Google Scholar 

  86. Optimal shapes for brittle beams under torsion (with H.F. Weinberger). In Complex Analysis and its Applications—Jubilee Volume for I.Y. Vekua, Nauka, Moscow, 1978, pp. 88–91.

    Google Scholar 

  87. Gradient estimates and Liouville theorems for quasi-linear elliptic equations (with L.A. Peletier). Ann. Scuola Norm. Sup. Pisa, 5, Ser. IV (1978), 65–104.

    MathSciNet  MATH  Google Scholar 

  88. The concepts of thermodynamics. In Continuum Mechanics and Partial Differential Equations (G.M. de la Penha et al., eds.). North-Holland, Amsterdam, 1978, pp. 411–451.

    Google Scholar 

  89. On the impossibility of linear Cauchy and Piola–Kirchhoff constitutive theories for stress in solids (with R.L. Fosdick). J. Elasticity, 9 (1979), 83–89.

    Article  MathSciNet  MATH  Google Scholar 

  90. Conceptual analysis of the classical second laws of thermodynamics. Arch. Rational Mech. Anal., 70 (1979), 254–272.

    Google Scholar 

  91. Foundations of thermodynamics. Lecture Notes, University of Naples, 1979 (150 pages, multiplied typescript).

    Google Scholar 

  92. Phase transitions and interfacial layers for van der Waals fluids. In Recent Methods in Nonlinear Analysis and Applications (Proc. Fourth International Meeting of SAFA), (A. Canfora et al., eds.). Liguori Editore, Naples, 1981, pp. 169–175.

    Google Scholar 

  93. The second law of thermodynamics for systems with approximate cycles (with B.D. Coleman and D.R. Owen). Arch. Rational Mech. Anal., 77 (1981), 103–142.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  94. Uniqueness of solutions of semilinear Poisson equations (with K. McLeod). Proc. Nat. Acad. Sci. USA, 78 (1981), 6592–6598. See also entry [114].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  95. Uniqueness of positive solutions of semilinear equations in ℝn (with L.A. Peletier), Archive Rational Mech. Anal., 81 (1983), 181–197. See also entry [110].

    MathSciNet  ADS  MATH  Google Scholar 

  96. The form of interfacial surfaces in Korteweg’s theory of phase equilibria. Quart. Appl. Math., 41 (1983), 357–364.

    Google Scholar 

  97. The mechanical theory of fluid interfaces and Maxwell’s rule (with E. Aifantis). J. Coll. Interface Sci., 96 (1983), 519–547.

    Google Scholar 

  98. The structure and laws of thermodynamics. Proc. International Congress of Mathematicians (Warsaw 1983), 1717–1728.

    Google Scholar 

  99. Applied mathematics and scientific thought. In Nonlinear Analysis and Optimization. Lecture Notes in Mathematics, vol. 1107, Springer-Verlag, New York, 1984, pp. 1927.

    Google Scholar 

  100. One-dimensional shock layers in Korteweg fluids (with R. Hagan). In Phase Transformations and Material Instabilities in Solids. Academic Press, New York, 1984, 113–128.

    Google Scholar 

  101. Extensions of the mountain pass theorem (with P. Pucci). J. Funct. Anal., 59 (1984), 185–210.

    Article  MathSciNet  MATH  Google Scholar 

  102. A mountain pass theorem (with P. Pucci). J. Differential Equations, 60 (1985), 142–149.

    Article  MathSciNet  MATH  Google Scholar 

  103. Esistenza ed unicità degli stati fondamentali per equazioni ellittiche quasilineari (with B. Franchi and E. Lanconelli). Rend. Accad. Naz. Lincei, Serie 8,79 (1985),121–126. See also entries [119], [150].

    MathSciNet  MATH  Google Scholar 

  104. A continuum model for chemical mixture dynamics. In Developments in Mechanics (Proc. Midwestern Mechanics Conference), vol. 13, 1985, pp. 59–64.

    Google Scholar 

  105. Non-existence theorems for quasi-linear partial differential equations (with W.-M. Ni). Suppl. Rend. Circolo Mat. Palermo, 8 (1985), 171–185.

    MATH  Google Scholar 

  106. On the thermomechanics of interstitial working (with J.E. Dunn). Arch. Rational Mech. Anal., 88 (1985), 95–133.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  107. An outline of thermodynamical structure. In New Perspectives in Thermodynamics, (J. Serrin, ed.). Springer-Verlag, New York, 1986, 3–32.

    Google Scholar 

  108. Existence and non—existence theorems for ground states of quasi-linear partial differential equations. The anomalous case (with W.-M. Ni). Accad. Naz. Lincei, Atti dei Convegni, 77 (1986), 231–257.

    Google Scholar 

  109. Dynamic changes of phase in a van der Waals fluids (with R. Hagan). In New Perspectives in Thermodynamics. ( J. Serrin, ed.). Springer-Verlag, New York, 1986, pp. 241–260.

    Google Scholar 

  110. Uniqueness of non-negative solutions of semilinear equations in ℝn (with L.A. Peletier). J. Differential Equations, 61 (1986), 380–397.

    Article  MathSciNet  MATH  Google Scholar 

  111. Non-existence of singular solutions of quasi-linear partial differential equations (with W.-M. Ni). Comm. Pure Appl. Math., 39 (1986), 379–399.

    Article  MathSciNet  MATH  Google Scholar 

  112. A general variational identity (with R. Pucci). Indiana Univ. Math. J., 35 (1986), 681–703.

    Article  MathSciNet  MATH  Google Scholar 

  113. The laws of thermodynamics. Rev. Mechanica, 21 (1987), 361–379.

    Google Scholar 

  114. Uniqueness of positive radial solutions of Δu + f (u)= 0 in ℝn (with K. McLeod). Arch. Rational Mech. Anal.,99 (1987), 115–145.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  115. The structure of the critical set in the mountain pass theory (with P. Pucci). Trans. Amer. Math. Soc., 229 (1987), 115–132.

    Article  MathSciNet  Google Scholar 

  116. Ground states for a prescribed mean curvature equation (with L.A. Peletier). Proc. Amer. Math. Soc., 100 (1987), 694–700.

    Article  MathSciNet  MATH  Google Scholar 

  117. Positive solutions of a prescribed mean curvature equation. In Calculus of Variations and Partial Differential Equations (S. Hildebrandt et. al., eds.). Lecture Notes in Mathematics, vol. 1340. Springer-Verlag, New York, 1988, pp. 248–255.

    Google Scholar 

  118. Ground states for the prescribed mean curvature equation: The supercritical case (with F.V. Atkinson and L.A. Peletier). In Nonlinear Diffusion Equations and Their Equilibrium States (I) (W.-M. Ni et al., eds.). MSRI Publ., vol. 12. Springer-Verlag, New York, 1988, pp. 51–74.

    Google Scholar 

  119. Existence and uniqueness of ground states of quasilinear elliptic equations (with B. Franchi and E. Lanconelli). In Nonlinear Diffusion Equations and Their Equilibrium States (I),MSRI Publ., vol. 12. Springer-Verlag, New York, 1988, pp. 293–300. See also entry [150].

    Google Scholar 

  120. Remarks on the first eigenspace for polyharmonic operators (with P. Pucci). Atti Sem. Mat. Fis. Univ. Modena, 36 (1988), 107–118.

    MathSciNet  MATH  Google Scholar 

  121. Asymptotic properties for solutions of strongly nonlinear ordinary differential equations (with P. Pucci). In Conference on Differential Equations and Geometry. Rend. Sem. Mat. Univ. Politec. Torino, Fascicolo Speciale, 1989, pp. 121–129.

    Google Scholar 

  122. Critical exponents and critical dimensions for the polyharmonic operator (with P. Pucci). J. Math. Pures Appl., 69 (1990), 55–83.

    MathSciNet  MATH  Google Scholar 

  123. Continuation and limit properties for solutions of strongly nonlinear second order differential equations (with P. Pucci). Asymptotic Anal., 4 (1991), 97–160.

    MathSciNet  MATH  Google Scholar 

  124. Bounds for vertical points of solutions of prescribed mean curvature type equations, II (with F.V. Atkinson and L.A. Peletier). Asymptotic Anal., 5 (1992), 283–310.

    MathSciNet  MATH  Google Scholar 

  125. The nature of thermodynamics. Atti Sem. Mat. Fis. Univ. Modena, 39 (1991), 445–472. Italian translation: Sulla natura della termodinamica. Atti e MemorieAccad. Naz. Scienze Lettre e Arti di Modena, Ser. VII, vol. 7 1992, pp. 185–202.

    Google Scholar 

  126. Global asymptotic stability for strongly nonlinear second order systems (with P. Pucci). In Nonlinear Diffusion Equations and Their Equilibrium States (III). (N.G. Lloyd et al., eds.). Birkhãuser, Boston, 1992, pp. 437–449

    Chapter  Google Scholar 

  127. Existence and non-existence for ground states of quasilinear elliptic equations (with H. Zou), Arch. Rational Mech. Anal., 121 (1992), 101–130.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  128. Precise damping conditions for global asymptotic stability for nonlinear second-order systems (with P. Pucci). Acta Math., 170 (1993), 275–307. See also entry [133].

    Article  MathSciNet  MATH  Google Scholar 

  129. IMA Vols. in Math. Appl., vol. 47. Springer-Verlag, New York, 1993, pp. 157–174.

    Google Scholar 

  130. The equations of continuum mechanics as a consequence of group invariance. In Advances in Continuum Mechanics, (G. Ferrarese, ed.). Pitagora Editrice, Bologna, 1993, pp. 217–225.

    Google Scholar 

  131. Asymptotic behavior of solutions of a nonstandard second-order differential equation (with W.A. Harris and P. Pucci). Differential Integral Equations, 6 (1993), 1201–1215.

    MathSciNet  MATH  Google Scholar 

  132. Existence and non-existence results for ground states of degenerate Laplace equations (with H. Zou). In Differential Equations with Applications to Mathematical Physics, vol. 192. Academic Press, New York, 1993, pp. 287–305.

    Chapter  Google Scholar 

  133. Precise damping conditions for global asymptotic stability of nonlinear second-order systems, II (with P. Pucci). J. Differential Equations, 113 (1994), 505–534.

    Article  MathSciNet  MATH  Google Scholar 

  134. Asymptotic stability for intermittently controlled nonlinear oscillators (with P. Pucci). SIAM J. Math. Anal., 25 (1994), 815–835.

    Article  MathSciNet  MATH  Google Scholar 

  135. On the derivation of Hamilton’s equations (with R Pucci). Arch. Rational Mech. Anal., 125 (1994), 297–310.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  136. Ground states of a quasi-linear equation (with L.A. Peletier and H. Zou). Differential Integral Equations, 7 (1994), 1063–1082.

    MathSciNet  MATH  Google Scholar 

  137. Asymptotic estimates for a nonstandard second-order differential equation (with W.A. Harris and P. Pucci). In Differential Equations, Dynamical Systems, and Control Science: A Festschrift in Honor of Lawrence Markus, (K.D. Elworthy et al., eds.). Lecture Notes in Pure and Applied Mathematics. Marcel Dekker, New York, 1994, pp. 75-85.

    Google Scholar 

  138. Classification of positive solutions of quasi-linear elliptic equations (with H. Zou). Topological Meth. Nonlinear Anal., 3 (1994), 1–26.

    MATH  Google Scholar 

  139. Asymptotic integration of second-order systems (with H. Zou). Amer. J. Math., 116 (1994), 1241–1264.

    Article  MathSciNet  MATH  Google Scholar 

  140. Bifurcation for semilinear equations at a singular limit (with F. Merle and L.A. Peletier). Indiana Univ. Math. J., 43 (1994), 585–605.

    Article  MathSciNet  MATH  Google Scholar 

  141. Non-existence of positive solutions of semilinear elliptic systems (with H. Zou). In A Tribute to Ilya Bakelman, (S.A. Fulling et al., eds.). Discourses in Mathematics and its Applications, vol. 3. Department of Mathematics, Texas A M University, 1994, pp. 56–69.

    Google Scholar 

  142. Space, Time, and Energy. Lectio Doctoralis at the University of Ferrara. In this volume.

    Google Scholar 

  143. Remarks on Lyapunov stability (with P. Pucci). Differential Integral Equations, 8 (1994), 1265–1278.

    MathSciNet  Google Scholar 

  144. A numerical study of the existence and non-existence of ground states and their bifurcation for the equations of Chipot and Weissler (with Y. Yan and H. Zou). Unpublished manuscript, 1994.

    Google Scholar 

  145. Reflections on mathematics. Lectio Doctoralis at the University of Padova. In “L’Anno Galileiano,” Vol. I. Ed. Lint, Trieste, 1995, pp. 120–124.

    Google Scholar 

  146. Asymptotic stability for ordinary differential systems with time dependent restoring potentials (with P. Pucci). Arch. Rational Mech. Anal., 132 (1995), 207–232.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  147. On the elementary thermodynamics of quasi-static systems and other remarks. In Thermoelastic Problems and the Thermodynamics of Continua. AMD-Vol. 198, 5362. Amer. Soc. Mech. Eng., Applied Mech. Div., 1995.

    Google Scholar 

  148. Quasi-variational systems. In First World Congress of Nonlinear Analysts (V. Lakshmikantham, ed.). De Gruyter, Berlin, 1996, pp. 2055–2068.

    Google Scholar 

  149. Asymptotic stability for non-autonomous damped wave systems (with P. Pucci). Comm. Pure Appl. Math., XLIX (1996), 177–216.

    Article  MathSciNet  Google Scholar 

  150. Existence and uniqueness of ground states of quasi-linear elliptic equations (with B. Franchi and E. Lanconelli). Adv. in Math., 118 (1996), pp. 177–143.

    Article  MathSciNet  MATH  Google Scholar 

  151. The Navier-Stokes equations and the laws of thermodynamics. Meccanica, 31 (1996), 546–563.

    Google Scholar 

  152. Stability for abstract evolution equations (with P. Pucci). In Partial Differential Equations and Applications, (P. Marcellini et al., eds.). Marcel Dekker, New York, 1996, 279–288.

    Google Scholar 

  153. Non-existence of positive solutions of Lane-Emden systems (with H. Zou). Differential Integral Equations, 9 (1996), 635–653.

    MathSciNet  MATH  Google Scholar 

  154. Global non-existence theorems for quasi-linear evolution equations with dissipation (with H. Levine). Arch. Rational Mech. Anal., 137 (1997), 341–361.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  155. Asymptotic stability for nonlinear parabolic systems (with P. Pucci). In Energy Mathods in Continuum Mechanics. Kluwer Academic, Dordrecht, 1996, pp. 66–74.

    Chapter  Google Scholar 

  156. Existence of positive solutions of the Lane-Emden system (with H. Zou). Atti Sem. Mat. Fis. Univ. Modena (1997). To appear.

    Google Scholar 

  157. Local asymptotic stability for dissipative wave systems (with P. Pucci). Israel J. Math. (1997). To appear.

    Google Scholar 

  158. Stability and blow-up for dissipative evolution equations (with P. Pucci). In Partial Differential Equations and Applications (G. Caristi and E. Mitidieri, eds.). Lecture Notes in Pure and Applied Math., vol. 177. Marcel Dekker, New York, 1977, pp. 279–288.

    Google Scholar 

  159. Some remarks on global non-existence for non-autonomous abstract evolution equations (with H. Levine and P. Pucci). Contemp. Math., 208 (1997), 253–263.

    MathSciNet  Google Scholar 

  160. Uniqueness of ground states for quasi-linear elliptic operators (with P. Pucci). To appear.

    Google Scholar 

  161. The existence of positive entire solutions of elliptic Hamiltonian systems (with H. Zou). To appear.

    Google Scholar 

  162. Global existence and nonexistence theorems for quasi-linear evolution equations of formally parabolic type (with H. Levine and S.R. Park), J. Diff. Eqs. To appear.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Pucci, P. (1998). An Appreciation of James Serrin. In: Buttazzo, G., Galdi, G.P., Lanconelli, E., Pucci, P. (eds) Nonlinear Analysis and Continuum Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2196-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2196-8_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7455-1

  • Online ISBN: 978-1-4612-2196-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics