Hölder Continuity of Harmonic Quasiconformal Mappings

Details Hölder Continuity of Harmonic Quasiconformal Mappings Hölder Continuity of Harmonic Quasiconformal Mappings

2010-12-14

arxiv.org/abs/1012.3145v4

Mathematics

Complex Variables

This is an updated version of the same paper - added two references and a sentence explaining relevance of these two papers. T

Scientific paper

We prove that for harmonic quasiconformal mappings $\alpha$-H\"older
continuity on the boundary implies $\alpha$-H\"older continuity of the map
itself. Our result holds for the class of uniformly perfect bounded domains, in
fact we can allow that a portion of the boundary is thin in the sense of
capacity. The problem for general bounded domains remains open.

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