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$ p$-harmonic functions in the plane


Author: Juan J. Manfredi
Journal: Proc. Amer. Math. Soc. 103 (1988), 473-479
MSC: Primary 35J60; Secondary 30C60, 31A30
DOI: https://doi.org/10.1090/S0002-9939-1988-0943069-2
MathSciNet review: 943069
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Abstract: Given $ p > 1$, let $ u$ be a solution to $ \operatorname{div}(\nabla u{\vert^{p - 2}}\nabla u) = 0$, on a domain $ \Omega $ of the plane. Using the theory of quasiregular mappings we prove that the zeros of $ \nabla u$ are isolated in $ \Omega $, obtain bounds for the Hölder exponent of $ \nabla u$ and prove a strong form of the comparison principle.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943069-2
Article copyright: © Copyright 1988 American Mathematical Society

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