On quasiconformal selfmappings of the unit disk and elliptic PDE in the plane

2010/09/06 by Kalaj, David
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1009.1133

Abstract

We prove the following theorem: if w is a quasiconformal mapping of the unit disk onto itself satisfying elliptic partial differential inequality |L[w]|≤ B|∇ w|²+Γ, then w is Lipschitz continuous. This result extends some recent results, where instead of an elliptic differential operator is only considered the Laplace operator.

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