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 conditions for the (K,K′)-quasiconformal solutions of the ᾱ-Poisson equation with a nonhomogeneous term to be Lipschitz continuous.
Keywordsweighted Laplacian operator Lipschitz continuity Dirichlet boundary problem harmonic mapping (K,K′)-quasiconformal mapping
MSC(2010)30C65 31A05 30C40 35J25
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This work was supported by National Natural Science Foundation of China (Grant No. 11471128), the Natural Science Foundation of Fujian Province of China (Grant No. 2016J01020), Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (Grant Nos. ZQN-YX110 and ZQN-PY402). The author is deeply indebted to Professor David Kalaj for his helpful suggestion about the study of Lipschitz continuity. The author is grateful to the anonymous referees for their careful reading of the manuscript and many helpful suggestions.
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