Advertisement

Boundary value problems for systems with Cauchy-Riemannian main part

  • Heinrich Begehr
V Section — Function Theoretical Methods In Functional Analysis (Operators And Differential Operators)
  • 222 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 1014)

Keywords

Elliptic System Quasiconformal Mapping Nonlinear Boundary Beltrami Equation Generalize Analytic Function 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Ahlfors, L. On quasi-conformal mappings. J. Analyse Math.3 (1954), 1–58.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [1]
    Begehr, H. Boundary value problems for analytic and generalized analytic functions. To appear in "Complex Analysis-methods, trends, and applications". Ed. E. Lanckau and W. Tutschke, Akademie-Verlag, Berlin.Google Scholar
  3. [1]
    Begehr, H.-Gilbert, R.P. Über das Randwert-Normproblem für ein nichtlineares elliptisches System. Lecture Notes in Math. 561, Springer Verlag 1976, 112–121.Google Scholar
  4. [2]
    Das Randwert-Normproblem für ein fastlineares elliptisches System und eine Anwendung. Ann. Acad. Sci. Fenn. AI, 3 (1977), 179–184.MathSciNetzbMATHGoogle Scholar
  5. [3]
    Randwertaufgaben ganzzahliger Charakteristik für verallgemeinerte hyperanalytische Funktionen. Appl. Anal. 6 (1977), 189–205.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [4]
    On Riemann boundary value problems for certain linear elliptic systems in the plane. J. Differential Equations 32 (1979), 1–14.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [1]
    Begehr, H.-Hile, G.N. Nonlinear Riemann boundary value problems for a nonlinear elliptic system in the plane, to appear in Math. Z.Google Scholar
  8. [2]
    Riemann boundary value problems for nonlinear elliptic systems, to the published.Google Scholar
  9. [1]
    Begehr, H.-Hsiao, G.C. On nonlinear boundary value problems for an elliptic system in the plane. Lecture Notes in Math. 846, Springer Verlag 1981, 55–63.Google Scholar
  10. [2]
    Nonlinear boundary value problems for a class of elliptic systems. Kmplexe Analysis und ihre Anwendung auf partielle Differentialgleichungen. Martin-Luther-Universität, Halle-Wittenberg 1980, 90–102.Google Scholar
  11. [3]
    Nonlinear boundary value problems of Riemann-Hilbert type, to appear in Proc. AMS special sesson on elliptic systems in the plane. 87 th annual meeting, San Francisco, January 1981.Google Scholar
  12. [4]
    A priori estimates for elliptic systems, to be published.Google Scholar
  13. [5]
    The Hilbert boundary value problem for nonlinear elliptic systems, to be published.Google Scholar
  14. [1]
    Bers, L. Function theoretic properties of solutions of partial differential equations of elliptic type. Ann. Math. Studies 33(1954), 69–94.MathSciNetzbMATHGoogle Scholar
  15. [1]
    Bers, L.-Nirenberg, L. One a representation theorem for linear elliptic systems with discontinuous coefficients and its applications. Conv. Eq. Lin. Derivate Partiali. Trieste 1954. Cremonense, Roma 1955, 111–140.Google Scholar
  16. [1]
    Bojarski, B. Generalized solutions of a system of differential equation of the first order of elliptic type with discontinuous coefficients. Math. Sbornik 43 (85) (1957), 451–503.MathSciNetGoogle Scholar
  17. [2]
    An abstract problem of linear conjugacy and Fredholm pairs of subspaces. Differential and integral equations. Boundary value problems. Tbilis. Gos. Univ., Tbilisi 1979, 45–60.Google Scholar
  18. [1]
    Bojarski, B.-Twaniec, T. Quasiconformal mappings and nonlinear elliptic equations in two variables. I–II. Bull. Acad. Polon. Sci. 22 (1974), 473–478, 479–484.MathSciNetGoogle Scholar
  19. [1]
    DĂzuraev, A. Systems of equations of composite type. Nauka, Moscow 1972 (Russian).Google Scholar
  20. [1]
    Gakhov, I.D. Boundary value problems. Pegamon, Oxford, 1966.zbMATHGoogle Scholar
  21. [1]
    Gilbert, R.P. Nonlinear boundary value problems for elliptic systems in the plane. Proc. Int. Conf. Nonlinear Systems Appl., ed. V. Lakshmikantham, 1977, Akademic Press, 97–124.Google Scholar
  22. [2]
    Verallgemeinerte hyperanalytische Funktionentheorie. Komplexe Analysis und ihre Anwendungen auf partielle Differentialgleichungen. Martin-Luther-Universität, Halle-Wittenberg 1980, 124–145.zbMATHGoogle Scholar
  23. [1]
    Gilbert, R.P.-Buchanan, J. The Hilbert problem for hyperanalytic functions. Univ. Delaware Techn. Report 66A.Google Scholar
  24. [1]
    Haack, W.-Wendland, W. Vorlesungen über partielle und Pfaffsche Differentialgleichungen. Birkhäuser-Verlag, Basel 1969.CrossRefzbMATHGoogle Scholar
  25. [2]
    Lectures on partial and Pfaffian differential equations. Pergamon Press, Oxford 1972.zbMATHGoogle Scholar
  26. [1]
    Mamourian, A. General transmission and boundary value problems for first order elliptic equations in multiply-connected plane domains. Demonstratio Math. 12 (1979), 785–802.MathSciNetzbMATHGoogle Scholar
  27. [1]
    Monahov, V.N. Boundary value problems with free boundaries for elliptic systems. Isdatel'ctvo Nauka Sib. Otdelenie Novocibirsk 1977. (Russian).Google Scholar
  28. [1]
    Muskhelishvili, N.I. Singular integral equations. Noordhoff, Groningen, 1953.zbMATHGoogle Scholar
  29. [1]
    Naas, J.-Tutschke, W. Some probabilistic aspects in partial complex differential equations. Complex analysis and its applications. Akad. Nauk SSSR, Moscow 1978, 409–412.Google Scholar
  30. [2]
    On the error in the approximate solution of boundary value problems of nonlinear first order differential equations in the plane. Appl. Anal. 7(1978), 239–246.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [1]
    Prössdorf, S. Einige Klassen singulärer Gleichungen. Akademieverlag Berlin 1974 und Birkhäuser Verlag 1974.Google Scholar
  32. [1]
    Simonenko, I.B. Some general questions in the theory of the Riemann boundary value problem. Isv. Akad. Nauk SSSR, Ser. Mat. 32 (1968), 1138–1146 (Russian).MathSciNetGoogle Scholar
  33. [1]
    Tjurikov, E.V. The nonlinear Riemann-Hilbert boundary value problem for quasilinear elliptic systems. Soviet Math. Dokl. 20 (1979), 863–866.Google Scholar
  34. [1]
    Tutschke, W. Die neuen Methoden der komplexen Analysis und ihre Anwendung auf nichtlineare Differentalgleichungssysteme. S.-ber. Akad. Wiss. DDR, 17 N (1976).Google Scholar
  35. [2]
    Lösung nichtlinearer partieller Differentialgleichungssysteme erster Ordnung in der Ebene durch Verwendung einer komplexen Normalform. Math. Nachr. 75 (1976), 283–298.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [3]
    The Riemann-Hilbert problem for nonlinear systems of differential equations in the plane. Complex analysis and its applications, Akad. Nauk SSSR, Moscow 1978, 537–542 (Russian).Google Scholar
  37. [4]
    Solutions with prescribed periods on the boundary components for non-linear elliptic systems of first order in multiply connected domains in the plane. Martin-Luther-Universität Halle, Preprint Nr. 27 (1979) 3–9.Google Scholar
  38. [5]
    Reduction of the problem of linear conjugation for first order nonlinear elliptic systems in the plane to an analogous problem for holomorphic functions. Lecture Notes of Math., Springer-Verlag, 798 (1980), 446–455.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [1]
    Vekua, I.N. Generalized analytic functions. Pergamon, London, 1962.zbMATHGoogle Scholar
  40. [1]
    Vinogradov, V.S. On a boundary value problem for linear elliptic systems of differential equations of the first order on the plane. Dokl. Akad. Nauk SSSR 118 (1958), 1059–1062 (Russian).MathSciNetzbMATHGoogle Scholar
  41. [2]
    Über die Beschränktheit der Lösungen von Randwertproblemen für lineare elliptische Systeme erster Ordnung in der Ebene. Dokl. Akad. Nauk SSSR 121 (1958), 399–402 (Russian).zbMATHGoogle Scholar
  42. [3]
    Über einige Randwertprobleme für quasilineare elliptische Systeme erster Ordnung in der Ebene. Dokl. Akad. Nauk SSSR 121 (1958), 579–581 (Russian).zbMATHGoogle Scholar
  43. [4]
    A certain boundary value problem for an elliptic system of special form. Differencial'nye Uravnenija 7 (1971), 1226–1234, 1341 (Russian).MathSciNetzbMATHGoogle Scholar
  44. [1]
    Wen, Guo-Chun On Riemann-Hilbert boundary value problems of elliptic systems of linear partial differential equations of the first order. Acta Math. Sinica 15 (1965), 599–613. (Chinese).zbMATHGoogle Scholar
  45. [2]
    On Riemann-Hilbert problems for nonlinear elliptic systems of first order in the plane. Acta Math. Sinica 23 (1980), 244–255 (Chinese).MathSciNetzbMATHGoogle Scholar
  46. [3]
    Modified Dirichlet problem and quasiconformal mappings for nonlinear elliptic systems of first order. Kexue Tongbao 25 (1980), 449–453.MathSciNetzbMATHGoogle Scholar
  47. [4]
    Function-theoretical properties of solutions for nonlinear elliptic complex equations of first order. Hebei Huagong Xueynan Xuebao Shuxue Zhuanji, 1980, 41–61.Google Scholar
  48. [5]
    The continuously differentiable solutions for nonlinear elliptic complex equations of first order. Hebei Huagong Xueynan Xuebao, Shuxue, Zhuanji, 1980, 62–83 (Chinese).Google Scholar
  49. [1]
    Wendland, W. An integral equation method for generalized analytic functions. Lecture Notes in Math., No. 430, Springer-Verlag 1974, 414–452.Google Scholar
  50. [2]
    On the imbedding method for semilinear first order elliptic systems and related finite element methods. Continuation Methods, ed. H. Wacker, Academic Press, 1977, 277–336.Google Scholar
  51. [3]
    Elliptic systems in the plane. Pitman Publishing, Inc., London, 1978.zbMATHGoogle Scholar
  52. [4]
    Numerische Methoden bei Randwertproblemen elliptischer Systeme in der Ebene. Komplexe Analysis und ihre Anwendungen auf partielle Differentialgleichungen. Martin-Luther-Universität, Halle-Wittenberg 1980, 310–348.Google Scholar
  53. [1a]
    v. Wolfersdorf, L. Monotonicity methods for a class of first order semilinear elliptic systems. Komplexe Analysis und ihre Anwendungen auf partielle Differentialgleichungen. Martin-Luther-Universität, Halle-Wittenberg 1980, 369–373.Google Scholar
  54. [1]
    Wolska-Bochenek, J. A compound nonlinear boundary value problem in the theory of pseudo-analytic functions. Demonstratio Math. 4 (1972), 105–117. Freie Univ. Berlin, I. Math. Institut, Hüttenweg 9, 1000 Berlin 33MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Heinrich Begehr

There are no affiliations available

Personalised recommendations