A pointwise comparison for solutions of linear elliptic equations
type: Item
instance of: scholarly article
title: A pointwise comparison for solutions of linear elliptic equations
zbMATH Open document ID: 0624.35025
author: Lucia Migliaccio
author: Diana Nunziante
published in: Ricerche di Matematica
publication date: 1985-01-01T00:00:00Z
review text: Comparison theorems are proved for solutions of two Dirichlet problems for second-order linear elliptic equations (1) \(Lu=f\) in a bounded domain \(G\subset {\mathbb{R}}^ n\), \(n\geq 2\). A weak solution \(u\in W_ 0^{1,2}(G)\) of (1) is compared with the solution v of a problem with radial symmetry. In particular, a pointwise comparison \(u^{\#}(x)\leq v(x)\) is obtained a.e. in a ball, where \(u^{\#}\) denotes the symmetric decreasing rearrangement of u.
reviewed by: Charles A. Swanson
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 4013135
zbMATH Keywords: Comparison
zbMATH Keywords: Dirichlet problems
zbMATH Keywords: weak solution
zbMATH Keywords: radial symmetry
zbMATH Keywords: symmetric decreasing rearrangement
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4013135