Weak maximum principle for elliptic operators on a stratified set
type: Item
instance of: scholarly article
title: Weak maximum principle for elliptic operators on a stratified set
zbMATH Open document ID: 1158.35331
author: A. A. Gavrilov
author: O. M. Penkin
published in: Journal of Mathematical Sciences (New York)
publication date: 2008-09-03T00:00:00Z
review text: Let \(\Omega \) be a connected set in \(\mathbb R^m\) which is the union of finitely many smooth manifolds (strata) \(\sigma_{ki}\) of different dimension. The subscript \(k\) is the dimension and the subscript \(i\) is the number of a stratum of this dimension. Strata regularly are adjacent to each other; if a stratum \(\sigma_{ki}\) is adjacent to \(\sigma_{k+1,j}\), then when a point \(y\in \sigma_{k+1,j}\) approaches a point \(x\in \sigma_{ki}\), the tangent space \(T_y \sigma_{k+1,j}\) tends to a certain limit position containing \(T_x \sigma_{k,i}\). The set \(\Omega \) has a cell complex structure. \(\Omega_0\) is a dense domain in \(\Omega \) composed of strata. For a nonnegative function \(q\) it is proved the weak maximum principle for a continuous function \(u\) on \(\Omega \) which solves the inequality \(L_q u \geq 0\) in \(\Omega_0\).
reviewed by: Dagmar Medková
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 58A35
Mathematics Subject Classification ID: 35R45
zbMATH DE Number: 5319761
zbMATH Keywords: weak maximum principle
zbMATH Keywords: elliptic operator
zbMATH Keywords: stratified set
zbMATH Keywords: cell complex structure
MaRDI profile type: Publication
full work available at URL: s10958-007-0117-2
OpenAlex ID: W2054087792
cites work: Q5630031
DOI: 10.1007/S10958-007-0117-2
Recommended article: Strong maximum principle for an elliptic operator on a stratified set
Recommended article: Q3836660
Recommended article: On the weak maximum principle for degenerate elliptic operators
Recommended article: The Weak Maximum Principle for Degenerate Elliptic Operators in Unbounded Domains
Recommended article: Q3400752
Recommended article: On the maximum principle for elliptic operators
Recommended article: The mean-value theorem for elliptic operators on stratified sets
Recommended article: The maximum principle for parabolic inequalities on stratified sets
Recommended article: On the maximum principle for elliptic operators in weighted spaces
Recommended article: The weak maximum principle for a class of strongly coupled elliptic differential systems
description: scientific article; zbMATH DE number 5319761