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On the Occasion of the 70th Birthday of Vladimir Maz’ya

  • Alberto Cialdea
  • Flavia Lanzara
  • Paolo E. Ricci
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 193)

Abstract

This volume includes a selection of lectures given at the International Workshop “Analysis, Partial Differential Equations and Applications”, held at the Mathematical Department of Sapienza University (Rome, June 30th–July 3rd, 2008), on the occasion of the 70th birthday of Vladimir Maz’ya.

Keywords

Elliptic Equation Dirichlet Problem 70th Birthday Boundary Integral Equation Parabolic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    Yu.D. Burago, V.G. Maz’ya, V.D. Sapožnikova, On the double layer potential for nonregular domains. (Russian) Dokl. Akad. Nauk SSSR 147, 1962, 523–525.Google Scholar
  2. [2]
    Ju.D. Burago, V.G. Maz’ya, V.D. Sapožnikova, On the theory of potentials of a double and a simple layer for regions with irregular boundaries. (Russian) 1966 Problems Math. Anal. Boundary Value Problems Integr. Equations 3–34, 1966.Google Scholar
  3. [3]
    Yu.D. Burago, V.G. Maz’ya, Certain Questions of Potential Theory and Function Theory for Regions with Irregular Boundaries. (Russian) Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 3, 1967, 152 pp; English translation: Potential Theory and Function Theory for Irregular Regions. Translated from Russian. Seminars in Mathematics, V.A. Steklov Mathematical Institute, Leningrad, Vol. 3 Consultants Bureau, New York 1969 vii+68 pp.Google Scholar
  4. [4]
    G. Cimmino, Nuovo tipo di condizioni al contorno e nuovo metodo di trattazione per il problema generalizzato di Dirichlet, Rend. Circ. Mat. Palermo, 61, 1937, 117–221.CrossRefGoogle Scholar
  5. [5]
    G. Fichera, On a unified theory of boundary value problems for elliptic-parabolic equations of second order, Comm. Pure Appl. Math. 13, 1960, 457–468.CrossRefMathSciNetGoogle Scholar
  6. [6]
    G. Fichera, V.G. Maz’ya, In honor of Professor Solomon G. Mikhlin on the occasion of his seventieth birthday, Applicable Analysis, 7, 1978, 167–170.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    G.I. Kresin, V.G. Maz’ya, On the maximum modulus principle for linear parabolic systems with zero boundary data. Functional Differential Equations 5:1–2, 1998, 165–181.MATHMathSciNetGoogle Scholar
  8. [8]
    W. Littman, G. Stampacchia, H.F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa (3) 17, 1963, 43–77.MATHMathSciNetGoogle Scholar
  9. [9]
    V.G. Maz’ya, Solution of Dirichlet’s problem for an equation of elliptic type, Dokl. Akad. Nauk SSSR 129, 1959, 257–260.MathSciNetGoogle Scholar
  10. [10]
    V.G. Maz’ya, Classes of domains and imbedding theorems for function spaces. Soviet Math. Dokl. 133:1, 1960, 882–885.MathSciNetGoogle Scholar
  11. [11]
    V.G. Maz’ya, Some estimates of solutions of second-order elliptic equations. Dokl. Akad. Nauk SSSR 137, 1961, 1057–1059.MathSciNetGoogle Scholar
  12. [12]
    V.G. Maz’ya, On the boundary regularity of solutions of elliptic equations and of a conformal mapping. Dokl. Akad. Nauk SSSR 152, 1963, 1297–1300.MathSciNetGoogle Scholar
  13. [13]
    V.G. Maz’ya, V.D. Sapožnikova, Solution of the Dirichlet and Neumann problems for irregular domains by potential-theoretic methods. Dokl. Akad. Nauk SSSR 159, 1964, 1221–1223.MathSciNetGoogle Scholar
  14. [14]
    V.G. Maz’ya, B.A. Plamenevskiï, On singular equations with a vanishing symbol. Dokl. Akad. Nauk SSSR 160, 1965, 1250–1253.MathSciNetGoogle Scholar
  15. [15]
    V.G. Maz’ya, On the modulus of continuity of a solution of the Dirichlet problem near an irregular boundary. 1966 Problems Math. Anal. Boundary Value Problems Integr. Equations, pp. 45–58 Izdat. Leningrad. Univ., Leningrad.Google Scholar
  16. [16]
    V.G. Maz’ya, The behavior near the boundary of the solution of the Dirichlet problem for an elliptic equation of the second order in divergence form. Mat. Zametki 2, 209–220.Google Scholar
  17. [17]
    V.G. Maz’ya, Examples of nonregular solutions of quasilinear elliptic equations with analytic coefficients. Funkcional. Anal. i Priložen. 2:3, 1968, 53–57.MathSciNetGoogle Scholar
  18. [18]
    V.G. Maz’ya, Weak solutions of the Dirichlet and Neumann problems. Trudy Moskov. Mat. Obhšč. 20, 1969, 137–172.Google Scholar
  19. [19]
    V.G. Maz’ya, The continuity at a boundary point of the solutions of quasi-linear elliptic equations. Vestnik Leningrad. Univ. 25:13, 1970, 42–55; English translation: Vestnik Leningrad. Univ. Math. 3, 1976, 225–242.MathSciNetGoogle Scholar
  20. [20]
    V.G. Maz’ya, The degenerate problem with an oblique derivative. Mat. Sb. (N.S.) 87(129), 1972, 417–454.MathSciNetGoogle Scholar
  21. [21]
    V.G. Maz’ya, B. Paneyah, Degenerate elliptic pseudo-differential operators and the problem with oblique derivative. Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiï. Trudy Moskov. Mat. Obšč. 31, 1974, 237–295.Google Scholar
  22. [22]
    V.G. Maz’ya, G.I. Kresin, The maximum principle for second-order strongly elliptic and parabolic systems with constant coefficients. Mat. Sb. (N.S.) 125(167):4, 1984, 458–480.MathSciNetGoogle Scholar
  23. [23]
    V.G. Maz’ya, J. Rossmann, On the Agmon-Miranda maximum principle for solutions of elliptic equations in polyhedral and polygonal domains. Ann. Global Anal. Geom. 9:3, 1991, 253–303.CrossRefMathSciNetGoogle Scholar
  24. [24]
    V.G. Maz’ya, S. Poborchi, Differentiable Functions on Bad Domains. World Scientific, 1997.Google Scholar
  25. [25]
    V. Maz’ya, In memory of Gaetano Fichera. Problemi Attuali dell’Analisi e della Fisica Matematica, 1–4, 2000, Aracne.Google Scholar
  26. [26]
    V. Maz’ya, The Wiener test for higher-order elliptic equations, Duke Mathematical Journal, 115:3, 2002, 479–512.CrossRefMathSciNetGoogle Scholar
  27. [27]
    V. Maz’ya, I. Verbitsky, The Schrödinger operator on the energy space: boundedness and compactness criteria, Acta Mathematica, 188, 2002, 263–302.CrossRefMathSciNetGoogle Scholar
  28. [28]
    V. Maz’ya, M. Shubin, Discreteness of spectrum and positivity criteria for Schrödinger operators, Annals of Mathematics, 162, 2005, 1–24.CrossRefMathSciNetGoogle Scholar
  29. [29]
    V. Maz’ya, M. Shubin, Can one see the fundamental frequency of a drum?, Letters in Mathematical Physics, 74, no. 2, 2005, 135–151.CrossRefMathSciNetGoogle Scholar
  30. [30]
    V. Maz’ya, I. Verbitsky, Infinitesimal form boundedness and Trudingers subordination for the Schrödinger operator, Inventiones Mathematicae, 161, 2005, 81–136.CrossRefMathSciNetGoogle Scholar
  31. [31]
    V. Maz’ya, Analytic criteria in the qualitative spectral analysis of the Schrödinger operator, Spectral theory and mathematical physics: a Festschrift in honor of Barry Simons 60th birthday, Proc. Sympos. Pure Math., Part 1, Amer. Math. Soc., Providence, RI, 76, pp. 257–288, 2007.MathSciNetGoogle Scholar
  32. [32]
    V. Maz’ya, A. Movchan, Uniform asymptotics of Greens kernels for mixed and Neumann problems in domains with small holes and inclusions, Sobolev Spaces in Mathematics III. Applications in Mathematical Physics, pp. 277–316, Springer, 2008.Google Scholar
  33. [33]
    V. Maz’ya, T. Shaposhnikova, Theory of Sobolev Multipliers with Applications to Differential and Integral Operators, Grundlehren der Mathematischen Wissenschaften, vol. 337, Springer, 2008.Google Scholar
  34. [34]
    V. Maz’ya, M. Mitrea, T. Shaposhnikova, The Dirichlet problem in Lipschitz domains with boundary data in Besov spaces for higher-order elliptic systems with rough coefficients, Journal de Mathématiques Pures et Appliquées, 2009, to appear.Google Scholar
  35. [35]
    V. Maz’ya, A. Movchan, Asymptotic treatment of perforated domains without homogenization, Math. Nachr. 2009, to appear.Google Scholar
  36. [36]
    C. Miranda, Equazioni alle Derivate Parziali di Tipo Ellittico, Springer, 1955.Google Scholar
  37. [37]
    F.G. Tricomi, Formula d’inversione dell’ordine di due integrazioni doppie “con asterisco”, Rend. Lincei, 3:6, 1926, 535–539.Google Scholar
  38. [38]
    F.G. Tricomi, Equazioni integrali contenenti il valor principale di un integrale doppio, Math. Zeitschrift, 27, 1927, 87–133.MATHCrossRefMathSciNetGoogle Scholar
  39. [B1]
    Vladimir Maz’ya, Boundary Integral Equations on Contours with Peaks, (with A. Soloviev), to appear in Birkhäuser.Google Scholar
  40. [B2]
    Theory of Sobolev Multipliers with Applications to Differential and Integral Operators, (with T. Shaposhnikova) Grundlehren der Mathematischen Wissenschaften, vol. 337, Springer, 2009.Google Scholar
  41. [B3]
    Jacques Hadamard, Legend of Mathematics (with T. Shaposhnikova). MCNMO Publishers, Moscow, 2008 (revised, extended, and authorized translation from English to Russian).Google Scholar
  42. [B4]
    Approximate Approximations (with G. Schmidt), American Mathematical Society, 2007.Google Scholar
  43. [B5]
    Sharp Real-Part Theorems. A Unified approach (with G. Kresin), Lecture Notes in Mathematics, No. 1903, Springer, 2007.Google Scholar
  44. [B6]
    Imbedding and Extension Theorems for Functions in Non-Lipschitz Domains (with S. Poborchi), St. Petersburg University Publishers, 2007.Google Scholar
  45. [B7]
    Jacques Hadamard, un Mathématicien Universel (with T. Shaposhnikova), EDP Sciences, Paris, 2005 (revised and extended translation from English).Google Scholar
  46. [B8]
    Linear Water Waves. A Mathematical Approach (with N. Kuznetsov and B. Vainberg), Cambridge University Press, 2002.Google Scholar
  47. [B9]
    Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations (with V. Kozlov and J. Rossmann), Mathematical Surveys and Monographs, vol. 85, American Mathematical Society, 2000.Google Scholar
  48. [B10]
    Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, vol. 2 (with S. Nazarov and B. Plamenevskij), Operator Theory. Advances and Applications, vol. 112, XXIII+323, Birkhäuser, 2000.Google Scholar
  49. [B11]
    Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains, vol. 1 (with S. Nazarov and B. Plamenevskij), Operator Theory. Advances and Applications, vol. 111, XXIII+435, Birkhäuser, 2000.Google Scholar
  50. [B12]
    Differential Equations with Operator Coefficients (with V. Kozlov), Springer Monographs in Mathematics, Springer-Verlag, 1999.Google Scholar
  51. [B13]
    Asymptotic Analysis of Fields in Multistructures (with V. Kozlov and A. Movchan), Oxford Science Publications, 1999.Google Scholar
  52. [B14]
    Jacques Hadamard, a Universal Mathematician (with T. Shaposhnikova), American Mathematical Society and London Mathematical Society, 1998.Google Scholar
  53. [B15]
    Differentiable Functions on Bad Domains (with S. Poborchi), World Scientific, 1997.Google Scholar
  54. [B16]
    Theory of a Higher-order Sturm-Liouville Equation (with V. Kozlov), Springer-Verlag, Lecture Notes in Mathematics, 1997.Google Scholar
  55. [B17]
    Elliptic Boundary Value Problems in Domains with Point Singularities (with V. Kozlov and J. Rossmann), American Mathematical Society, 1997.Google Scholar
  56. [B18]
    Asymptotische Theorie Elliptischer Randwertaufgaben in Singulär Gestörten Gebieten II (with S. Nazarov and B. Plamenevskii), Berlin, Akademie Verlag, Bd. 2, 1992.Google Scholar
  57. [B19]
    Asymptotische Theorie Elliptischer Randwertaufgaben in Singulär Gestörten Gebieten I (with S. Nazarov and B. Plamenevskii), Berlin, Akademie Verlag, 1991.Google Scholar
  58. [B20]
    Elliptic Boundary Value Problems (with N. Morozov, B. Plamenevskii, L. Stupyalis), American Mathematical Society Translations, Ser. 2, Vol. 123, 1984, AMS.Google Scholar
  59. [B21]
    Encyclopaedia of Mathematical Sciences, Vol. 27, Analysis IV, Linear and Boundary Integral Equations, V.G. Maz’ya, S.M. Nikol’skii (Eds.), Contributors: V.G. Maz’ya, S. Prössdorf, Springer-Verlag, 1991, V.G. Maz’ya: Boundary Integral Equations.Google Scholar
  60. [B22]
    Encyclopaedia of Mathematical Sciences, Vol. 26, Analysis III, Spaces of Differentiable Functions, S.M. Nikol’skii (Ed.), Contributors: L.D. Kudryavtsev, V.G. Maz’ya, S.M. Nikol’skii, Springer-Verlag, 1990, V.G. Maz’ya: Classes of Domains, Measures and Capacities in the Theory of Differentiable Functions.Google Scholar
  61. [B23]
    Theory of Multipliers in Spaces of Differentiable Functions (with T. Shaposhnikova), Pitman, 1985 (Russian version: Leningrad University Press, 1986).Google Scholar
  62. [B24]
    Sobolev Spaces, Springer-Verlag, 1985 (Russian version: Leningrad University Press, 1985).Google Scholar
  63. [B25]
    Abschätzungen fur Differentialoperatoren im Halbraum (with I. Gelman), Berlin, Akademie Verlag, 1981; Birkhäuser, 1982.Google Scholar
  64. [B26]
    Zur Theorie Sobolewsche Räume, Series: Teubner-Texte zur Mathematik BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1981.Google Scholar
  65. [B27]
    Einbettungssätze für Sobolewsche Räume, Teil 2, Series: Teubner-Texte zur Mathematik, Band 28, BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1980.Google Scholar
  66. [B28]
    Einbettungssätze für Sobolewsche Räume, Teil 1, Series: Teubner-Texte zur Mathematik BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 1979.Google Scholar
  67. [B29]
    Potential Theory and Function Theory for Irregular Regions (with Yu. Burago) Seminars in Mathematics, Steklov Institute, Leningrad, Vol. 3, Consultants Bureau, New York, 1969 (Russian version: 1967).Google Scholar
  68. [H1]
    Vladimir Maz’ya, Two volumes of “The Maz’ya Anniversary Collection”, edited by Rossmann, J., Takač, P., Wildenhain, Birkhäuser, 1999 (Vol. 1: On Maz’ya’s Work in Functional Analysis, Partial Differential Equations and Applications; Vol. 2: Rostock Conference on Functional Analysis, Partial Differential Equations and Applications).Google Scholar
  69. [H2]
    Mathematical Aspects of Boundary Element Methods, dedicated to Vladimir Maz’ya on the occasion of his 60th birthday, edited by M. Bonnet, A.M. Sändig and W. Wendland, Chapman & Hall/CRC Research Notes in Mathematics, London, 1999.Google Scholar
  70. [H3]
    Perspectives in Partial Differential Equations, Harmonic Analysis and Applications: A Volume in Honor of Vladimir G. Maz’ya’s 70th Birthday, edited by D. Mitrea and M. Mitrea, Proc. of Symposia in pure mathematics, Vol. 79, Amer. Math. Soc., Providence (R.I.), 2008.Google Scholar
  71. [H4]
    D. Eidus, A. Khvoles, G. Kresin, E. Merzbach, S. Prößdorf, T. Shaposhnikova, P. Sobolevskii, Mathematical work of Vladimir Maz’ya (on the occasion of his 60th birthday), Funct. Differ. Equ. 4 (1997), no. 1-2, pp. 3–11.MATHMathSciNetGoogle Scholar
  72. [H5]
    M.S. Agranovich, Yu.D. Burago, V.P. Khavin, V.A. Kondratiev, V.P. Maslov, S.M. Nikol’skii, Yu.G. Reshetnyak, M.A. Shubin, B.R. Vainberg, M.I. Vishik, L.R. Volevich, Vladimir G. Maz’ya, On the occasion of his 65th birthday, Russian Journal of Mathematical Physics, Vol. 10, No. 3, 2003, pp. 239–244.Google Scholar
  73. [H6]
    M.S. Agranovich, Yu.D. Burago, B.R. Vainberg, M.I. Vishik, S.G. Gindikin, V.A. Kondrat’ev, V.P. Maslov, S.V. Poborchii, Yu.G. Reshetnyak, V.P. Khavin, M.A. Shubin, Vladimir Gilelevich Maz’ya (on his 70th birthday), Russian Math. Surveys 63:1(2008), 189–196.MATHCrossRefMathSciNetGoogle Scholar
  74. [H7]
    Journal Vestnik St. Petersburg University: Mathematics 41:4, 2008.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Alberto Cialdea
    • 1
  • Flavia Lanzara
    • 2
  • Paolo E. Ricci
    • 2
  1. 1.Dipartimento di Matematica e InformaticaUniversità della BasilicataPotenzaItaly
  2. 2.Dipartimento di MatematicaSapienza Università di RomaRomaItaly

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