On the Dirichlet problemfor the Beltrami equation

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...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2014-04, Vol.122 (1), p.113-141
Main Authors: Kovtonyuk, D., Petkov, I., Ryazanov, V., Salimov, R.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Dirichlet problem
Dynamical Systems and Ergodic Theory
Functional Analysis
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary: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.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-014-0005-x