A priori estimates for some elliptic equations involving the p-Laplacian. (June 2018) - Damascelli, Lucio; Pardo, Rosa
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.