English

H\"older Continuity of Harmonic Quasiconformal Mappings

Complex Variables 2011-05-30 v4

Abstract

We prove that for harmonic quasiconformal mappings α\alpha-H\"older continuity on the boundary implies α\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.

Keywords

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