Singularities of a solution on a boundary of lower dimension
type: Item
instance of: scholarly article
title: Singularities of a solution on a boundary of lower dimension
zbMATH Open document ID: 0881.35004
DOI: 10.1007/BF02986897
author: G. Puriushkis
published in: Lithuanian Mathematical Journal
publication date: 1997-10-30T00:00:00Z
review text: Suppose that \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with boundary \(\Gamma_{n-1}\cup \Gamma_{n-2}\), where \(\Gamma_{n-1}\) and \(\Gamma_{n-2}\) are \((n-1)\)-dimensional and \((n-2)\)-dimensional, respectively, smooth manifolds, \(\Gamma_{n-1}\) and \(\Gamma_{n-2}\) do not intersect, \(n>2\), and \(P(x,D)\) is a linear differential operator in \(\Omega\) with smooth coefficients on \(\Omega\cup\Gamma_{n-2}\), \(\deg P(x,D)= m\), \(m\geq 2\). We consider the following problem: \[ P(x, D)u(x)=0,\quad x\in\Omega,\quad u(x)= 0,\quad x\in\Gamma_{n-2}\backslash A,\tag{1} \] where \(A\) is a closed set strictly inside \(\Gamma_{n-2}\). We consider the singularity of the solution on the set \(A\), i.e., the case where \(u(x)=0\) on \(\Gamma_{n-2}\), if \(u(x)\) is the solution of problem (1).
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 35G15
zbMATH DE Number: 1059807
zbMATH Keywords: Green formula
MaRDI profile type: Publication
cites work: Removable singularities of solutions of linear partial differential equations
cites work: Q3994619
full work available at URL: https://doi.org/10.1007/bf02986897
OpenAlex ID: W2055315542
description: scientific article; zbMATH DE number 1059807