Skip to main content
SpringerLink
Log in

Boundary value problems for systems with Cauchy-Riemannian main part

  • V Section — Function Theoretical Methods In Functional Analysis (Operators And Differential Operators)
  • Conference paper
  • First Online:
Complex Analysis — Fifth Romanian-Finnish Seminar

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1014))

  • 302 Accesses

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahlfors, L. On quasi-conformal mappings. J. Analyse Math.3 (1954), 1–58.

    Article  MathSciNet  MATH  Google Scholar 

  2. 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. 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. Das Randwert-Normproblem für ein fastlineares elliptisches System und eine Anwendung. Ann. Acad. Sci. Fenn. AI, 3 (1977), 179–184.

    MathSciNet  MATH  Google Scholar 

  5. Randwertaufgaben ganzzahliger Charakteristik für verallgemeinerte hyperanalytische Funktionen. Appl. Anal. 6 (1977), 189–205.

    Article  MathSciNet  MATH  Google Scholar 

  6. On Riemann boundary value problems for certain linear elliptic systems in the plane. J. Differential Equations 32 (1979), 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  7. 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. Riemann boundary value problems for nonlinear elliptic systems, to the published.

    Google Scholar 

  9. 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. 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. 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. A priori estimates for elliptic systems, to be published.

    Google Scholar 

  13. The Hilbert boundary value problem for nonlinear elliptic systems, to be published.

    Google Scholar 

  14. Bers, L. Function theoretic properties of solutions of partial differential equations of elliptic type. Ann. Math. Studies 33(1954), 69–94.

    MathSciNet  MATH  Google Scholar 

  15. 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. 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.

    MathSciNet  Google Scholar 

  17. 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. 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.

    MathSciNet  Google Scholar 

  19. DĂzuraev, A. Systems of equations of composite type. Nauka, Moscow 1972 (Russian).

    Google Scholar 

  20. Gakhov, I.D. Boundary value problems. Pegamon, Oxford, 1966.

    MATH  Google Scholar 

  21. 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. Verallgemeinerte hyperanalytische Funktionentheorie. Komplexe Analysis und ihre Anwendungen auf partielle Differentialgleichungen. Martin-Luther-Universität, Halle-Wittenberg 1980, 124–145.

    MATH  Google Scholar 

  23. Gilbert, R.P.-Buchanan, J. The Hilbert problem for hyperanalytic functions. Univ. Delaware Techn. Report 66A.

    Google Scholar 

  24. Haack, W.-Wendland, W. Vorlesungen über partielle und Pfaffsche Differentialgleichungen. Birkhäuser-Verlag, Basel 1969.

    Book  MATH  Google Scholar 

  25. Lectures on partial and Pfaffian differential equations. Pergamon Press, Oxford 1972.

    MATH  Google Scholar 

  26. Mamourian, A. General transmission and boundary value problems for first order elliptic equations in multiply-connected plane domains. Demonstratio Math. 12 (1979), 785–802.

    MathSciNet  MATH  Google Scholar 

  27. Monahov, V.N. Boundary value problems with free boundaries for elliptic systems. Isdatel'ctvo Nauka Sib. Otdelenie Novocibirsk 1977. (Russian).

    Google Scholar 

  28. Muskhelishvili, N.I. Singular integral equations. Noordhoff, Groningen, 1953.

    MATH  Google Scholar 

  29. 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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  31. Prössdorf, S. Einige Klassen singulärer Gleichungen. Akademieverlag Berlin 1974 und Birkhäuser Verlag 1974.

    Google Scholar 

  32. 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).

    MathSciNet  Google Scholar 

  33. Tjurikov, E.V. The nonlinear Riemann-Hilbert boundary value problem for quasilinear elliptic systems. Soviet Math. Dokl. 20 (1979), 863–866.

    Google Scholar 

  34. 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. Lösung nichtlinearer partieller Differentialgleichungssysteme erster Ordnung in der Ebene durch Verwendung einer komplexen Normalform. Math. Nachr. 75 (1976), 283–298.

    Article  MathSciNet  MATH  Google Scholar 

  36. 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. 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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  39. Vekua, I.N. Generalized analytic functions. Pergamon, London, 1962.

    MATH  Google Scholar 

  40. 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).

    MathSciNet  MATH  Google Scholar 

  41. 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).

    MATH  Google Scholar 

  42. Über einige Randwertprobleme für quasilineare elliptische Systeme erster Ordnung in der Ebene. Dokl. Akad. Nauk SSSR 121 (1958), 579–581 (Russian).

    MATH  Google Scholar 

  43. A certain boundary value problem for an elliptic system of special form. Differencial'nye Uravnenija 7 (1971), 1226–1234, 1341 (Russian).

    MathSciNet  MATH  Google Scholar 

  44. 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).

    MATH  Google Scholar 

  45. On Riemann-Hilbert problems for nonlinear elliptic systems of first order in the plane. Acta Math. Sinica 23 (1980), 244–255 (Chinese).

    MathSciNet  MATH  Google Scholar 

  46. Modified Dirichlet problem and quasiconformal mappings for nonlinear elliptic systems of first order. Kexue Tongbao 25 (1980), 449–453.

    MathSciNet  MATH  Google Scholar 

  47. 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. 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. Wendland, W. An integral equation method for generalized analytic functions. Lecture Notes in Math., No. 430, Springer-Verlag 1974, 414–452.

    Google Scholar 

  50. 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. Elliptic systems in the plane. Pitman Publishing, Inc., London, 1978.

    MATH  Google Scholar 

  52. 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. 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. 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 33

    MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Heinrich Begehr
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Cabiria Andreian Cazacu Nicu Boboc Martin Jurchescu Ion Suciu

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Begehr, H. (1983). Boundary value problems for systems with Cauchy-Riemannian main part. In: Cazacu, C.A., Boboc, N., Jurchescu, M., Suciu, I. (eds) Complex Analysis — Fifth Romanian-Finnish Seminar. Lecture Notes in Mathematics, vol 1014. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072085

Download citation

  • DOI: https://doi.org/10.1007/BFb0072085

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12683-6

  • Online ISBN: 978-3-540-38672-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation