A boundary value problem for the~Laplacian with rapidly changing type of~boundary conditions in a~multidimensional domain
type: Item
instance of: scholarly article
title: A boundary value problem for the~Laplacian with rapidly changing type of~boundary conditions in a~multidimensional domain
zbMATH Open document ID: 0939.35048
published in: Siberian Mathematical Journal
publication date: 2000-04-16T00:00:00Z
review text: In the article under review, the authors study boundary value problems for the Laplacian in \(\mathbb R^n\), \(n\leq 3\), with rapidly changing boundary conditions. As in the case of \(n=2\) considered in [\textit{G. A. Chechkin}, Mat. Sb., 184, No. 6, 99-150 (1993; Zbl 0875.35009)], the explicit form of the limit problem depends on the asymptotic behavior of the first eigenvalue of the spectral problem for the Laplacian operator that is cellular. An essential part of the article is devoted to studying the indicated asymptotic behavior for \(n\geq 3\). The authors use the methods worked out by Oleĭnik.
reviewed by: Vladimir N. Grebenev
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35P20
zbMATH DE Number: 1432310
zbMATH Keywords: Laplace equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: rapidly changing type of boundary conditions
zbMATH Keywords: asymptotic behavior of the minimal eigenvalue
zbMATH Keywords: rate of convergence of solutions
author: R. R. Gadyl'shin
author: G. A. Chechkin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1432310