On the boundary behavior of solutions of the Beltrami equations

We show that any homeomorphic solution of the Beltrami equation v from the Sobolev class W loc 1,1 is a so-called lower Q -homeomorphism with Q ( z ) =  K μ ( z ), where K μ ( z ) is the dilatation ratio of this equation. On this basis, we develop the theory of boundary behavior and removing of sing...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 63; no. 8; pp. 1241 - 1255
Main Authors Kovtonyuk, D. A., Petkov, I. V., Ryazanov, V. I.
Format Journal Article
LanguageEnglish
Published Boston Springer US 2012
Springer
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
Continuous Extension
Boundary Behavior
Quasiconformal Mapping
Sobolev Class
Beltrami Equation
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Summary:We show that any homeomorphic solution of the Beltrami equation v from the Sobolev class W loc 1,1 is a so-called lower Q -homeomorphism with Q ( z ) =  K μ ( z ), where K μ ( z ) is the dilatation ratio of this equation. On this basis, we develop the theory of boundary behavior and removing of singularities of these solutions.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-012-0575-7