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). |
|
摘要点击次数: 2621 |
全文下载次数: 1905 |
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. |
查看全文 查看/发表评论 下载PDF阅读器 |