Boundary-contact problems for domains with edge singularities
type: Item
instance of: scholarly article
title: Boundary-contact problems for domains with edge singularities
zbMATH Open document ID: 1136.35026
author: D. Kapanadze
author: B.-W. Schulze
published in: Journal of Differential Equations
publication date: 2007-03-12T00:00:00Z
full work available at URL: 2005 14.pdf
review text: Let \(G\) be a bounded domain in the Euclidean space of the form \(G= G_+\cup G_-\cup S\) for open subdomains \(G_+\), \(G_-\) of \(G\), such that \(\overline G_+\cap\overline G_-= S\) is an interface of codimension 1. Assume \(G_+\) is inside \(G\), namely \(\partial G_+= S\), \(S\cap\partial G= \emptyset\) and therefore \(\partial G_-= S\cup\partial G\). Starting from a pair of elliptic partial differential operators \(A_+\), \(A_-\) in \(G_+\), \(G_-\) respectively, the authors consider the boundary value problem: \(A_+ u_+= f_+\) in \(G_+\), \(A_- u_-= f_-\) in \(G_-\), \(Tu_-= h\) on \(\partial G\), \(T_+ u_++ T_- u_-= g\) on \(S\), where \(T\), \(T_+\), \(T_-\) are suitable Shapiro-Lopatinsky trace operators. The main focus of the paper is the case when \(G_+\) and \(G_-\) are manifolds with edges \(Y\subset S\); in this case \(S\) itself is a closed manifold with edge singularity \(Y\). A precise study of the problem is given in terms of pseudo-differential calculus, by using the techniques of \textit{B.-W. Schulze} [Boundary value problems and singular pseudo-differential operators. Wiley, Chichester (1998; Zbl 0907.35146)].
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 58J32
Mathematics Subject Classification ID: 58J40
zbMATH DE Number: 5132866
zbMATH Keywords: boundary-conpact problems
zbMATH Keywords: pseudo-differential operators
zbMATH Keywords: manifolds with edge singularity
zbMATH Keywords: edge spaces
zbMATH Keywords: asymptotics of solutions
reviewed by: Luigi Rodino
MaRDI profile type: Publication
OpenAlex ID: W1997178831
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DOI: 10.1016/J.JDE.2006.10.016
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description: scientific article; zbMATH DE number 5132866