Smoothness of a conformal mapping on a subset of the boundary (Q2817038)
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scientific article; zbMATH DE number 6620045
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Smoothness of a conformal mapping on a subset of the boundary |
scientific article; zbMATH DE number 6620045 |
Statements
Smoothness of a conformal mapping on a subset of the boundary (English)
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29 August 2016
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conformal mappings
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Hölder classes
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pseudoanalytic continuation
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0.9718613
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0.93136495
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0.9151158
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0.9133602
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0.9128838
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0.91014886
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Let \(f\) be a conformal mapping of the unit disk \(D\) onto a Jordan domain \(G\). A classical subject in geometric function theory is the study of the relation of the smoothness of \(f\) (up to the boundary) and the smoothness of the boundary of \(G\). The author studies what effect on the smoothness of \(f\) has the assumption that some part of the boundary of \(G\) has higher Hölder regularity than the rest of the boundary (a precise statement appears in the article, of course). The proof is based on the concept pseudoanalytic continuation introduced by E. M. Dynkin.
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