Regularity of radial minimizers of reaction equations involving the p-Laplacian

Details Regularity of radial minimizers of reaction equations involving the p-Laplacian Regularity of radial minimizers of reaction equations involving the p-Laplacian

2007-12-17

arxiv.org/abs/0712.2788v1

Calc. Var. Partial Differential Equations 34 (2009), no. 4, 475--494.

Mathematics

Analysis of PDEs

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Scientific paper

We consider semi-stable, radially symmetric, and decreasing solutions of a reaction equation involving the p-Laplacian, where the reaction term is a locally Lipschitz function, and the domain is the unit ball. For this class of radial solutions, which includes local minimizers, we establish pointwise and Sobolev estimates which are optimal and do not depend on the specific nonlinear reaction term. Under standard assumptions we also prove the regularity of the corresponding extremal solution.

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