Radial symmetry of solutions to diffusion equations with discontinuous\n nonlinearities

2011/01/26 by Joaquim Serra, Serra, Joaquim
Mathematics · Computer Science · Engineering · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1101.5094

Abstract

We prove a radial symmetry result for bounded nonnegative solutions to the\np-Laplacian semilinear equation -\Δ_p u=f(u) posed in a ball of\n mathbb Rⁿ and involving discontinuous nonlinearities f. When p=2 we\nobtain a new result which holds in every dimension n for certain positive\ndiscontinuous f. When p\≥ n we prove radial symmetry for every locally\nbounded nonnegative f. Our approach is an extension of a method of P. L.\nLions for the case p=n=2. It leads to radial symmetry combining the\nisoperimetric inequality and the Pohozaev identity.\n

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