$p$-harmonic functions in the plane
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- by Juan J. Manfredi PDF
- Proc. Amer. Math. Soc. 103 (1988), 473-479 Request permission
Abstract:
Given $p > 1$, let $u$ be a solution to $\operatorname {div}(\nabla u{|^{p - 2}}\nabla u) = 0$, 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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- 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