Problem of conjugation of harmonic functions in three-dimensional domains with nonsmooth boundaries
type: Item
instance of: scholarly article
title: Problem of conjugation of harmonic functions in three-dimensional domains with nonsmooth boundaries
zbMATH Open document ID: 1022.31004
author: I. T. Denisyuk
published in: Russian Mathematics
publication date: 2003-07-30T00:00:00Z
review text: The author deals with a problem that arises from the theory of continuum media: A finite number of disjoint, simply connected domains \(V_1, V_2,\dots, V_k\) in \(\mathbb R^3\) is given. These domains are bounded by closed surfaces \(S_1, S_2,\dots,S_k\) and each such surface contains a finite number of singular points (angular and conic points). The problem is to construct harmonic functions \(F_0, F_1, \dots, F_k\) such that \(F_j\) is harmonic in \(V_j\), \(j=1, 2,\dots, k\), and \(F_0\) is harmonic in \(\mathbb R^3\setminus \bigcup_{j=1}^k V_j\), and these functions must satisfy certain boundary conditions on the surfaces \(S_j\) (conditions of conjugation) of Dirichlet-Neumann-Robin type. The author investigates the solvability of the problem using single and double layer potentials.
reviewed by: Dimitrios Betsakos
Mathematics Subject Classification ID: 31B05
Mathematics Subject Classification ID: 31B20
zbMATH DE Number: 1956429
zbMATH Keywords: harmonic function
zbMATH Keywords: conjugation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1956429