Boundary integral equations of the logarithmic potential theory for domains with peaks
type: Item
instance of: scholarly article
title: Boundary integral equations of the logarithmic potential theory for domains with peaks
zbMATH Open document ID: 0865.35027
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1997-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/244221
review text: Dirichlet and Neumann boundary value problems are considered for the Laplacian on a plane domain whose boundary is smooth except for a finite number of peaks. Peaks are points where arcs of the boundary meet at zero angle. Following the classical method, solutions are represented in the form of single and double layer potentials. This paper develops the theory of the corresponding boundary integral equations for the densities of the potentials. Fredholm theory is not applicable in the presence of peaks and an alternative approach is used, based on auxiliary boundary value problems. Theorems on unique solvability and asymptotic representations near peaks are presented. For a class of functions with a weak power singularity, the kernels of the integral operators are found.
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 915282
zbMATH Keywords: nonsmooth domain
zbMATH Keywords: single layer potential
zbMATH Keywords: double layer potentials
zbMATH Keywords: unique solvability
zbMATH Keywords: asymptotic representations near peaks
author: V. Maz'ya
author: Alexander A. Solov'ev
reviewed by: Alan J. Pryde
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 915282