On the Dirichlet problemfor the Beltrami equation

被引：2

作者：

Kovtonyuk, D. ^{[1
]}

Petkov, I. ^{[1
]}

Ryazanov, V. ^{[1
]}

Salimov, R. ^{[1
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Appl Math & Mech, UA-83114 Donetsk, Ukraine

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2014年 / 122卷

关键词：

EXTREMAL LENGTH; ELLIPTIC-EQUATIONS; BMO;

D O I：

10.1007/s11854-014-0005-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that homeomorphic W (loc) (1,1) solutions of the Beltrami equations satisfy certain modular inequalities. On this basis, we develop the theory of the boundary behavior of such solutions and prove a series of criteria for the existence of regular, pseudoregular and multi-valued solutions for the Dirichlet problem to the Beltrami equation in Jordan domains and finitely connected domains, respectively. These results have important applications to various problems of mathematical physics.

引用

页码：113 / 141

页数：29

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