QCH mappings between unit ball and domain with $C^{1,\alpha}$ boundary

Anton Gjokaj; David Kalaj

QCH mappings between unit ball and domain with $C^{1,\alpha}$ boundary

Analysis of PDEs 2021-03-19 v2

Authors: Anton Gjokaj , David Kalaj

Abstract

We prove the following. If $f$ is a harmonic quasiconformal mapping between the unit ball in $\mathbb{R}^n$ and a spatial domain with $C^{1,\alpha}$ boundary, then $f$ is Lipschitz continuous in $B$ . This generalizes some known results for $n=2$ and improves some others in higher dimensional case.

Keywords

lipschitz spaces pseudoconvex domains harmonic functions

Cite

@article{arxiv.2005.05667,
  title  = {QCH mappings between unit ball and domain with $C^{1,\alpha}$ boundary},
  author = {Anton Gjokaj and David Kalaj},
  journal= {arXiv preprint arXiv:2005.05667},
  year   = {2021}
}

Comments

This version contains corrections of some minor errors

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