The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks
type: Item
instance of: scholarly article
title: The solution of the third problem for the Laplace equation on planar domains with smooth boundary and inside cracks and modified jump conditions on cracks
zbMATH Open document ID: 1215.35052
DOI: 10.1155/IJMMS/2006/91983
author: Dagmar Medková
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2007-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/45093
review text: Summary: This paper studies the third problem for the Laplace equation on a bounded planar domain with inside cracks. The third condition \(\partial u/\partial n+hu=f\) is given on the boundary of the domain. The skip of the function \(u_{+} - u_{ - }=g\) and the modified skip of the normal derivatives \((\partial u/\partial n)_+ - (\partial u/\partial n)_- +hu_{+}=f\) are given on cracks. The solution is looked for in the form of the sum of a modified single-layer potential and a double-layer potential. The solution of the corresponding integral equation is constructed.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35Q74
zbMATH DE Number: 5164244
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5164244