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Chen, Jiaolong; Li, Peijin; Sahoo, Swadesh Kumar; Wang, Xiantao

On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains. (English) Zbl 1379.30012

Isr. J. Math. 220, No. 1, 453-478 (2017).
Authors’ 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.
Reviewer: Matti Vuorinen (Turku)

Cited in 9 Documents

MSC:

30C62 Quasiconformal mappings in the complex plane

Keywords:

quasiconformal maps
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References:

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