H\"older Continuity of Harmonic Quasiconformal Mappings
Complex Variables
2011-05-30 v4
Abstract
We prove that for harmonic quasiconformal mappings -H\"older continuity on the boundary implies -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.
Cite
@article{arxiv.1012.3145,
title = {H\"older Continuity of Harmonic Quasiconformal Mappings},
author = {Miloš Arsenović and Vesna Manojlović and Matti Vuorinen},
journal= {arXiv preprint arXiv:1012.3145},
year = {2011}
}
Comments
This is an updated version of the same paper - added two references and a sentence explaining relevance of these two papers. The last version: corrected typos, restricted to dimension at least 3