Quasiregular families bounded in L^p and elliptic estimates

2018/06/03 by Aimo Hinkkanen, Hinkkanen, Aimo, Gaven Martin +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV

paper · pdf · doi:10.48550/arxiv.1806.00758

arxiv created 2018/06/03 · arxiv updated 2018/06/05

Abstract

We prove that a family of quasiregular mappings of a domain Ω 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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