Skip to main content
SpringerLink
Log in

The Riemann-Hilbert Problem for First Order Complex Equations of Mixed Type

  • Chapter
Partial Differential and Integral Equations

Part of the book series: International Society for Analysis, Applications and Computation ((ISAA,volume 2))

  • 483 Accesses

Abstract

In this paper we discuss the Riemann-Hilbert boundary value problem for first order linear complex equations of mixed(elliptic-hyperbolic) type in a simply connected domain. Firstly, we give a representation theorem and prove the uniqueness of solutions for the above boundary value problem, afterwards by using the method of successive iteration, the existence of solutions for the above problem is proved. In [1], A.V. Bitsadze discussed the Tricomi problem for some mixed equation of second order. By using the results in the present paper, we can derive the results from [1].

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bitsadze, A.V.: Some classes of partial differential equations. Gordon and Breach, New York, etc., 1988.

    MATH  Google Scholar 

  2. Wen, Guo-chun, Begehr, H.: Boundary value problems for elliptic equations and systems. Longman Scientific and Technical, Harlow, 1990.

    MATH  Google Scholar 

  3. Wen, Guo-chun: Conformal mappings and boundary value problems. Amer. Math. Soc., Providence, RI, 1992.

    Google Scholar 

  4. Begehr, H., Wen, Guo-chun: Nonlinear elliptic boundary value problems and their applications. Addison Wesley Longman, Harlow, 1996.

    MATH  Google Scholar 

  5. Wen, Guo-chun: Some boundary value problems for linear mixed complex equations of first and second order. J. Yantai Univ, 1997, no.3, 157–164 (Chinese).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Peking University, Beijing, 100871, China

    Guo-Chun Wen

Authors
  1. Guo-Chun Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Freie Universität Berlin, Berlin, Germany

    Heinrich G. W. Begehr

  2. University of Delaware, Newark, Delaware, USA

    Robert P. Gilbert

  3. Peking University, Beijing, China

    Guo-Chun Wen

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Kluwer Academic Publishers

About this chapter

Cite this chapter

Wen, GC. (1999). The Riemann-Hilbert Problem for First Order Complex Equations of Mixed Type. In: Begehr, H.G.W., Gilbert, R.P., Wen, GC. (eds) Partial Differential and Integral Equations. International Society for Analysis, Applications and Computation, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3276-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3276-3_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3278-7

  • Online ISBN: 978-1-4613-3276-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation