Solution of the transmission problem
type: Item
instance of: scholarly article
title: Solution of the transmission problem
zbMATH Open document ID: 1204.31005
author: Dagmar Medková
published in: Acta Applicandae Mathematicae
publication date: 2010-05-19T00:00:00Z
review text: The solution of the following transmission problem for the Laplace equation is constructed: \(\Delta u_{+} =0 \) on \( G^{+}\), \( \Delta u_{-} =0 \) in \(G^-\), \( u_{+}-u_{-} =f \) in \(\partial G^{+}\), \(n \cdot (\nabla u_+ - a \nabla u_{-})+b \tau \cdot (\nabla u_{+} - \nabla u_{-})+h_+ u_+ + h_-u_- = g\) on \(\partial G^+\), where \(G^+ \) and \(G^- \) are complementary domains with connected Lipschitz boundary, \(a \) is a positive constant, \(h^+ \) and \(h^- \) are nonnegative functions belonging to a suitable Lebesgue space on \(\partial G^+ \), as \( f \) and \( g \), and \(\tau \) is a measurable field of unit tangent vectors on \(\partial G^+.\)
reviewed by: Maria Alessandra Ragusa
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 5709158
zbMATH Keywords: transmission problem
zbMATH Keywords: Laplace equation
zbMATH Keywords: explicit solution
zbMATH Keywords: single layer potential
zbMATH Keywords: double layer potential
MaRDI profile type: Publication
full work available at URL: s10440-009-9522-5
OpenAlex ID: W2047207946
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DOI: 10.1007/S10440-009-9522-5
description: scientific article; zbMATH DE number 5709158