Riemann-Hilbert Problem and Its Well-Posed-Ness for Elliptic Complex Equations of First Order in Multiply Connected Domains  

作　　者：Guochun WE Liping WANG 

机构地区：[1]LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,P. R. China [2]College of Mathematics and Information Science,Hebei Normal University,Hebei 050024,P. R. China

出　　处：《Journal of Mathematical Research with Applications》2014年第4期435-445,共11页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11171349);the Science Foundation of Hebei Province(Grant No.A2010000346)

摘　　要：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.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.

关 键 词：Riemann-Hilbert problems quasilinear elliptic complex equations multiply connected domains priori estimates and existence of solutions. 

分 类 号：O175.25[理学—数学]