Quasiregular families bounded in $L^p$ and elliptic estimates

Aimo Hinkkanen; Gaven Martin

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arXiv · 1806.00758

Quasiregular families bounded in $L^p$ and elliptic estimates

Aimo Hinkkanen·Gaven Martin

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Abstract

We prove that a family of quasiregular mappings of a domain $\Omega$ which are uniformly bounded in $L^p$ for some $p>0$ form a normal family. From this we show how an elliptic estimate on a functional differences implies all directional derivatives, and thus the complex gradient to be quasiregular. Consequently the function enjoys much higher regularity than apriori assumptions suggest.

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BibTeX RIS

Aimo Hinkkanen, Gaven Martin. 2018-06-03. Quasiregular families bounded in $L^p$ and elliptic estimates. https://arxiv.org/abs/1806.00758

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