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Lipschitz continuity for solutions of the ᾱ-Poisson equation

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In this paper, we study the Lipschitz continuity for solutions of the ᾱ-Poisson equation. After characterizing the boundary conditions for the Lipschitz continuity of ᾱ-harmonic mappings, we present four equivalent… Click to show full abstract

In this paper, we study the Lipschitz continuity for solutions of the ᾱ-Poisson equation. After characterizing the boundary conditions for the Lipschitz continuity of ᾱ-harmonic mappings, we present four equivalent conditions for the (K,K′)-quasiconformal solutions of the ᾱ-Poisson equation with a nonhomogeneous term to be Lipschitz continuous.

Keywords: poisson equation; lipschitz continuity; solutions poisson; continuity solutions

Journal Title: Science China Mathematics
Year Published: 2019

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