Existence of bounded solutions for non linear elliptic unilateral problems

Abstract

This paper proves the existence of (at least) one solution of the following variational inequality: {Mathematical expression} Here A is an operator of Leray-Lions type acting from W01,p(Ω) into W-1,p′(Ω) and H grows like |Du|p. The obstacle ψ is a measurable function with values in {Mathematical expression}, the only hypothesis being {Mathematical expression}. This allows ψ to be -∞, recovering the case where (*) is an equation. Finally there is no smoothness assumptions on the data: Ω is a bounded open set in RN, A and H are defined from Carathéodory functions. © 1988 Fondazione Annali di Matematica Pura ed Applicata.