Existence results for nonlinear elliptic equations
type: Item
instance of: scholarly article
title: Existence results for nonlinear elliptic equations
zbMATH Open document ID: 1008.35023
author: V. M. Monetti
author: Loredana Randazzo
published in: Ricerche di Matematica
publication date: 2002-12-17T00:00:00Z
review text: Existence results are proved for the problem \(Au+g(x,u,Du)+H(x,Du)=f\), \(u\in W^{1,p}_0 (\Omega)\) where \(\Omega\) is a bounded set, \(A\) is a Leray-Lions operator; the function \(g(x,u,t)\) is a nonlinear lower-order term having \(p\)-growth \((p>1)\) in \(t\) and satisfies a sign condition with respect to \(u\), while the function \(H(x,t)\) grows at most as \(|t|^{p-1}\). A priori estimates for the solution are obtained using symmetrization techniques. Then a sequence of approximate problems is considered and a priori estimates are found. This allows to pass to the limit in the sequence of approximate problems.
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 1846829
zbMATH Keywords: nonlinear elliptic equations
zbMATH Keywords: measure data
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1846829