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arXiv · 1512.06330

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

Jiaolong Chen·Peijin Li·Swadesh Kumar Sahoo·Xiantao Wang
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Abstract

We first investigate the Lipschitz continuity of $(K, K')$-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 $(K, K')$-quasiregular mappings, and as the other application, we study the Lipschitz continuity of $(K,K')$-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, Mateljevi\'{c} and Pavlovi\'{c}.

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Jiaolong Chen, Peijin Li, Swadesh Kumar Sahoo, Xiantao Wang. 2015-12-20. On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains. https://arxiv.org/abs/1512.06330

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