| 闻国椿,王丽萍.多连通区域上一阶椭圆型复方程的Riemann-Hilbert问题与其适定性[J].数学研究及应用,2014,34(4):435~445 |
| 多连通区域上一阶椭圆型复方程的Riemann-Hilbert问题与其适定性 |
| Riemann-Hilbert Problem and Its Well-Posed-Ness for Elliptic Complex Equations of First Order in Multiply Connected Domains |
| 投稿时间：2013-04-22 修订日期：2014-02-24 |
| DOI：10.3770/j.issn:2095-2651.2014.04.006 |
| 中文关键词: Riemann-Hilbert问题 拟线性椭圆型复方程 多连通区域 先验估计与解的存在性. |
| 英文关键词:Riemann-Hilbert problems quasilinear elliptic complex equations multiply connected domains priori estimates and existence of solutions. |
| 基金项目:国家自然科学基金(Grant No.11171349),河北省科学基金(Grant No.A2010000346). |
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| 中文摘要: |
| 本文, 我们首先提出了多连通区域上一阶一致椭圆型复方程的Riemann-Hilbert问题与其适定性; 然后, 我们给出有关修正的复方程的Riemann-Hilbert问题解的积分表示, 并且还获得了修正的复方程的Riemann-Hilbert问题解的先验估计与可解性; 最后, 我们得到了原边值问题的可解性结果. |
| 英文摘要: |
| 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. |
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