On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains

Abstract

We first investigate the Lipschitz continuity of $(K,K^{\prime })$-quasiregular $C^2$ mappings between two Jordan domains with smooth boundaries, satisfying certain partial differential inequalities concerning Laplacian. Then two applications of the obtained result are given: As a direct consequence, we get the Lipschitz continuity of $\rho$-harmonic $(K,K^{\prime })$-quasiregular mappings, and as the other application, we study the Lipschitz continuity of $(K,K^{\prime })$-quasiconformal self-mappings of the unit disk, which are the solutions of the Poisson equation $\Delta w=g$. These results generalize and extend several recently obtained results by Kalaj, Mateljević and Pavlović.

20 pages

Cited by in corpus (1)

• Representation formula and bi-Lipschitz continuity of solutions to inhomogeneous biharmonic Dirichlet problems in the unit disk