Quasiregular families bounded in $L^p$ and elliptic estimates
Complex Variables
2018-06-05 v1
Abstract
We prove that a family of quasiregular mappings of a domain which are uniformly bounded in for some 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.
Keywords
Cite
@article{arxiv.1806.00758,
title = {Quasiregular families bounded in $L^p$ and elliptic estimates},
author = {Aimo Hinkkanen and Gaven Martin},
journal= {arXiv preprint arXiv:1806.00758},
year = {2018}
}