Lipschitz continuity of quasiconformal mappings and of the solutions to second order elliptic PDE with respect to the distance ratio metric

TL;DR

This paper investigates the Lipschitz continuity of specific quasiconformal mappings and solutions to certain elliptic PDEs relative to the distance ratio metric, providing insights into their regularity properties.

Contribution

It establishes Lipschitz continuity results for $(K, K')$-quasiconformal mappings and solutions to quasilinear elliptic PDEs in the context of the distance ratio metric.

Findings

Lipschitz continuity of $(K, K')$-quasiconformal mappings established

Lipschitz continuity of solutions to quasilinear elliptic PDEs demonstrated

Results enhance understanding of regularity in quasiconformal and elliptic PDE contexts

Abstract

The main aim of this paper is to study the Lipschitz continuity of certain $(K, K')$-quasiconformal mappings with respect to the distance ratio metric, and the Lipschitz continuity of the solution of a quasilinear differential equation with respect to the distance ratio metric.