A priori estimates for some elliptic equations involving the p-Laplacian

2017/09/16 by Damascelli, Lucio, Pardo, Rosa · 1 citation
#35B09 #35B33 #35B45 #35J62 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.05537

Abstract

We consider the Dirichlet problem for positive solutions of the equation -Δ_p (u) = f(u) in a convex, bounded, smooth domain Ω⊂\R^N, with f locally Lipschitz continuous. \par We provide sufficient conditions guarantying L^∞ a priori bounds for positive solutions of some elliptic equations involving the p-Laplacian and extend the class of known nonlinearities for which the solutions are L^∞ a priori bounded. As a consequence we prove the existence of positive solutions in convex bounded domains.

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