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Radial symmetry of the first eigenfunction for the $ p$-Laplacian in the ball


Author: Tilak Bhattacharya
Journal: Proc. Amer. Math. Soc. 104 (1988), 169-174
MSC: Primary 35P30; Secondary 35J60
MathSciNet review: 958061
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Abstract: We prove the radial symmetry of the eigenfunction corresponding to the first eigenvalue of the equation: $ \operatorname{div}\left( {\vert\nabla u{\vert^{p - 2}}\nabla u} \right) + \lambda \vert u{\vert^{p - 2}}u = 0$, when $ \Omega $ is a ball in $ {R^n}$ and $ 1 < p < \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0958061-1
Article copyright: © Copyright 1988 American Mathematical Society