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

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.