On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains
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We first investigate the Lipschitz continuity of (K,K’)-quasiregular C2 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 ρ-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 Δw = g. These results generalize and extend several recently obtained results by Kalaj, Mateljević and Pavlović.
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