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

Daners, Daniel; Drábek, Pavel

doi:10.1090/S0002-9947-09-04839-9

A priori estimates for a class of quasi-linear elliptic equations
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Trans. Amer. Math. Soc. 361 (2009), 6475-6500 Request permission

Abstract:

In this paper we prove 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. We finally prove estimates for solutions to equations with non-linear source and show that, under suitable growth conditions, all solutions are globally bounded.

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