A priori estimates for a class of quasi-linear elliptic equations

Daniel Daners and Pavel Drábek

Preprint, February 2007
Transactions of the American Mathematical Society, 361(2009), 6475-6500.
Original article at doi:10.1090/S0002-9947-09-04839-9
Citations on Google Scholar

Abstract

In this paper we prove new a priori estimates for a class of quasi-linear elliptic equations. To make the proofs clear and transparent we concentrate on the p-Laplacian. We focus on L_p-estimates for weak solutions of the problem with all standard boundary conditions on non-smooth domains. As an application we prove existence, continuity and compactness of the resolvent operator.

AMS Subject Classification (2000): 35B45, 35B65, 35J65, 35J70

To request a preprint please contact me.

You can go to the original article.