Skip to main content
Log in

Nonlinear Riemann boundary value problems for a nonliear elliptic system in the plane

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Begehr, H., Gilbert, R.P.: On Riemann boundary value problems for certain linear elliptic systems in the plane. J. Differential Equations32, 1–14 (1979)

    Google Scholar 

  2. Begehr, H., Gilbert, R.P.: Piecewise continuous solutions of pseudoparabolic equations in two space dimensions. Proc. Roy. Soc. Edinburgh Sect. A81, 153–173 (1978)

    Google Scholar 

  3. Begehr, H., Hsiao, G.C.: On nonlinear boundary value problems for an elliptic system in the plane. In: Ordinary and Partial Differential Equations. Proceedings of the Sixth Conference Held at Dundee, Scottland 1980, pp. 55–63. Lecture Notes in Mathematics846. Berlin-Heidelberg-New York: Springer 1981

    Google Scholar 

  4. Bojarskii, B.: Theory of generalized analytic vectors. Ann. Polon. Math.17, 281–320 (1966)

    Google Scholar 

  5. Bojarskii, B.: Quasiconformal mappings and general structural properties of systems of nonlinear equations elliptic in the sense of Lavrent'ev. Inst. Naz. Alta Mat. Symposia Math.18, 485–499 (1976)

    Google Scholar 

  6. Bojarskii, B., Iwaniec, T.: Quasiconformal mappings and non-linear elliptic equations in two variables I–II. Bull. Acad. Polon. Sci. Sér Sci. Math. Astronom. Phys.22, 473–478, 479–484 (1974)

    Google Scholar 

  7. Gakhov, I.D.: Boundary Value Problems. Oxford: Pergamon 1966

    Google Scholar 

  8. Gilbert, R.P.: Nonlinear boundary value problems for elliptic systems in the plane. Technical Report63, Newark: University of Delaware 1977

    Google Scholar 

  9. Gilbert, R.P., Hile, G.N.: Generalized hypercomplex function theory. Trans. Amer. Math. Soc.195, 1–29 (1974)

    Google Scholar 

  10. Iwaniec, T.: Quasiconformal mapping problem for general nonlinear systems of partial differential equations. Inst. Naz. Alta Mat. Symposia Math.18, 501–517 (1976)

    Google Scholar 

  11. Muskhelishvili, N.I.: Singular Integral Equations, Groningen: Noordhoff 1953

    Google Scholar 

  12. Nass, J., Tutschke, W.: Some probabilistic aspects in partial complex differential equations. In: Complex analysis and its applications. Proceedings (Moscow 1978), pp. 409–412. Moscow: Akad. Nauk SSSR 1978

    Google Scholar 

  13. Schaefer, H., Über die Methode der a priori-Schranken. Math. Ann.129, 415–416 (1955)

    Google Scholar 

  14. Tutschke, W., The Riemann Hilbert problem for nonlinear systems of differential equations in the plane. In: Complex analysis and its applications, Proceedings (Moscow 1978), pp. 537–542. Moscow: Akad. Nauk SSSR 1978 [Russian]

    Google Scholar 

  15. Tutschke, W.: Die neuen Methoden der komplexen Analysis und ihre Anwendung auf nichtlineare DGI-Systeme. S.-ber. Akad. Wiss. DDR, 17N (1976)

  16. Vekua, I.N.: Generalized Analytic Functions. London: Pergamon 1962

    Google Scholar 

  17. Wacker, H.J.: Eine Lösungsmethode zur Behandlung nichtlinearer Randwertprobleme. In: Iterationsverfahren, Numerische Mathematik, Approximationstheorie. Vortragsauszüge von Tagungen (Oberwolfach 1968, 1968, 1969) pp. 245–257. Basel-Stuttgart: Birkhäuser 1970

    Google Scholar 

  18. Warowna-Dorau, G.: Application of the method of successive approximations to a non-linear Hilbert problem in the class of generalized analytic functions. Demonstratio Math.2, 101–116 (1970)

    Google Scholar 

  19. Wendland, W.: An integral equation method for generalized analytic functions. In: Constructive and Computational Methods for Differential and Integral Equations. Symposium at Indiana University (Bloomington 1974), pp. 414–452. Lecture Notes in Mathematics430, Berlin-Heidelberg-New York: Springer 1974

    Google Scholar 

  20. Wendland, W.: Elliptic Systems in the Plane. London: Pitman 1978

    Google Scholar 

  21. Wendland, W.: On a class of semilinear boundary value problems for certain elliptic systems in the plane. In: Complex analysis and its applications. Proceedings (Moscow 1978), pp. 108–119. Moscow: Akad. Nauk SSSR 1978

    Google Scholar 

  22. Wendland, W.: On the imbedding method for semilinear first order elliptic systems and related finite element methods. Continuation Methods (ed. H. Wacker). Proceedings of a Symposium (Linz 1977) pp. 277–336. New York-London: Academic Press 1978

    Google Scholar 

  23. Wolska-Bochenek, J.: A compound non-linear boundary value problem in the theory of pseudo-analytic functions. Demonstratio Math.4, 105–117 (1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The second author was supported in part by National Science Foundation grant MCS78-01993 and by a fellowship from the Humboldt Foundation of West Germany, while visiting at the Free University of Berlin in 1979

Rights and permissions

Reprints and permissions

About this article

Cite this article

Begehr, H., Hile, G.N. Nonlinear Riemann boundary value problems for a nonliear elliptic system in the plane. Math Z 179, 241–261 (1982). https://doi.org/10.1007/BF01214316

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01214316

Keywords

Navigation