Journal of Inequalities and Applications
Volume 3 (1999), Issue 2, Pages 109-125
doi:10.1155/S1025583499000077

L∞-estimates for nonlinear elliptic problems with p-growth in the gradient

V. Ferone,1 M. R. Posteraro,1 and J. M. Rakotoson2

1Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico ll”, Via Cintia – Complesso Monte S. Angelo, Napoli 80126, Italy
2Département de Mathématiques, Université de Poitiers, 40, Avenue du Recteur Pineau, Poitiers 86022, France

Received 18 September 1997; Revised 20 January 1998

Copyright © 1999 V. Ferone et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the Dirichlet problem for a class of nonlinear elliptic equations whose model is −div(|∇u|p−2∇u)=|∇u|p+g−divf. We give a prioriL∞-estimates using symmetrization methods. An obstacle problem for nonlinear variational inequalities is also studied.