A priori estimates for some elliptic equations involving the p-Laplacian. (June 2018)

• Record Type: Journal Article
• Authors: Damascelli, Lucio; Pardo, Rosa
• Is Part Of: Nonlinear analysis. Volume 41(2018)
• Page Start: 475
• Page End: 496
• Publication Date: 2018-06
• Subjects: A priori estimates -- Quasilinear elliptic equations with p-Laplacian -- Critical Sobolev exponent -- Moving planes method -- Pohozaev identity -- Picone identity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.11.003
• Languages: English
• ISSNs: 1468-1218

Abstract

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. We provide sufficient conditions guaranteeing 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.