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arXiv · 1709.06305

Quasiconformal mappings and H\"older continuity

David Kalaj·Arsen Zlaticanin
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Abstract

We establish that every $K$-quasiconformal mapping $w$ of the unit ball $\IB$ onto a $C^2$-Jordan domain $\Omega$ is H\"older continuous with constant $\alpha= 2-\frac{n}{p}$, provided that its weak Laplacean $\Delta w$ is in $ L^p(\IB)$ for some $n/2<p<n$. In particular it is H\"older continuous for every $0<\alpha<1$ provided that $\Delta w\in L^n(\IB)$.

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David Kalaj, Arsen Zlaticanin. 2017-09-19. Quasiconformal mappings and H\"older continuity. https://arxiv.org/abs/1709.06305

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