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 Word: Riemann-Hilbert problems   quasilinear elliptic complex equations   multiply connected domains   priori estimates and existence of solutions.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11171349) and the Science Foundation of Hebei Province (Grant No.A2010000346).
Author NameAffiliation
Guochun WEN LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China 
Liping WANG College of Mathematics and Information Science, Hebei Normal University, Hebei 050024, P. R. China 
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      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.
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