| Riemann-Hilbert Problem and Its Well-Posed-Ness for Elliptic Complex Equations of First Order in Multiply Connected Domains |
| Received:April 22, 2013 Revised:February 24, 2014 |
| Key Words:
Riemann-Hilbert problems quasilinear elliptic complex equations multiply connected domains priori estimates and existence of solutions.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11171349) and the Science Foundation of Hebei Province (Grant No.A2010000346). |
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| Abstract: |
| In this article, we first propose the Riemann-Hilbert problem for uniformly elliptic complex equations of first order and its well-posed-ness in multiply connected domains. Then we give the integral representation of solutions for modified Riemann-Hilbert problem of the complex equations. Moreover we shall obtain a priori estimates of solutions of the modified Riemann-Hilbert problem and verify its solvability. Finally the solvability results of the original boundary value problem can be obtained. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.04.006 |
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