Existence and regularity results for p-Laplacian boundary value problems
type: Item
instance of: scholarly article
title: Existence and regularity results for p-Laplacian boundary value problems
zbMATH Open document ID: 1310.35125
author: Lourdes Moreno-Mérida
author: Lucio Boccardo
published in: S\(\vec{\text{e}}\)MA Journal
publication date: 2015-01-21T00:00:00Z
review text: The main purpose of the paper is to introduce some of the main tools to study nonlinear boundary value problems. In particular, the Dirichlet problem for the \(p\)-Laplace operator is concerned, which is the simplest example. The paper is divided into four sections. After introductory section, the second one deals with existence and regularity results when the right hand side belongs to the dual space of \(W^{1,p}(D)\). In this case, the model problem (P) is a variational boundary value problem. In Sections 3 and 4 the problem (P) is considered, when the right hand side is a function which does not belong to the dual space \(W_{0}^{1,p}(D)\). Next, the existence of distributional solutions belonging to a function space strictly contained in \(W_{0}^{1,1}(D)\) is shown. On the other hand, it is proved the existence of solutions belonging to \(W_{0}^{1,1}(D)\) and not belonging to \(W_{0}^{1,q}(D ), 1<q<p\). It is pointed out that existence results of \(W_{0}^{1,1}(D)\) distributional solutions is not so usual in elliptic problems.
Mathematics Subject Classification ID: 35J66
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6388851
zbMATH Keywords: nonlinear boundary value problems
zbMATH Keywords: weak solutions
zbMATH Keywords: distributional solutions
reviewed by: Stepan Agop Tersian
MaRDI profile type: Publication
full work available at URL: s40324-014-0021-x
OpenAlex ID: W2010128891
cites work: Q3457964
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DOI: 10.1007/S40324-014-0021-X
description: scientific article; zbMATH DE number 6388851