Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators
type: Item
instance of: scholarly article
title: Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators
zbMATH Open document ID: 1208.35068
DOI: 10.4171/JEMS/210
author: Dario D. Monticelli
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2010-05-26T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: The paper deals with maximum principles for a class of linear elliptic differential operators of the second order with noncharacteristic degeneracy. The aim of the paper is to extend some important results from the uniformly elliptic setting to the above class of linear differential operators. Namely, under suitable hypothesis on the degeneracy set of the operator, the weak and strong maximum principles and Hopf type lemma are proved for classical solutions in bounded domains. Some a priori estimates for the solutions of Dirichlet problems are derived. As an example, the Grushin operator is considered. A partial symmetry result for classical solutions of semilinear problems on bounded, symmetric, and suitably convex domains and a nonexistence result for classical solutions of semilinear equations with subcritical growth defined on the whole space are proved as well.
reviewed by: G. Jaiani
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J61
zbMATH DE Number: 5712416
zbMATH Keywords: maximum principles
zbMATH Keywords: elliptic differential operators with noncharacteristic degeneracy
zbMATH Keywords: Grushin operator
MaRDI profile type: Publication
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OpenAlex ID: W2087818945
description: scientific article; zbMATH DE number 5712416