An average effect of many tiny holes in nonlinear boundary value problems with monotone boundary conditions
type: Item
instance of: scholarly article
title: An average effect of many tiny holes in nonlinear boundary value problems with monotone boundary conditions
zbMATH Open document ID: 0633.35028
author: Satoshi Kaizu
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: \textit{H. Attouch} [Variational convergence of functions and operators (1984; Zbl 0561.49012)] has investigated the magnitude effect of many tiny holes, whose shapes are not spherical in general, to the potential term of the Dirichlet problem for the Laplace equation using the notion of capacity. The author extends this method to a different type of boundary conditions, replacing capacity by a different class of magnitude.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4030057
zbMATH Keywords: tiny holes
zbMATH Keywords: potential term
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: Laplace equation
zbMATH Keywords: capacity
reviewed by: E. Paliokas
MaRDI profile type: Publication
full work available at URL: pjaa.62.133
OpenAlex ID: W2081143594
cites work: Q5186236
cites work: Q3961204
cites work: Q4120903
cites work: The Robin problems on domains with many tiny holes
cites work: A monotone boundary condition for a domain with many tiny spherical holds
cites work: Potential and scattering theory on wildly perturbed domains
DOI: 10.3792/PJAA.62.133
Recommended article: Q3834400
Recommended article: The Poisson Equation with Nonautonomous Semilinear Boundary Conditions in Domains with Many Time Holes
Recommended article: Homogenization of a class of elliptic problems with nonlinear boundary conditions in domains with small holes
Recommended article: Homogenization of nonlinear degenerate non-monotone elliptic operators in domains perforated with tiny holes
Recommended article: Q3218478
Recommended article: Homogenization of eigenvalue problems for the laplace operator with nonlinear terms in domains in many tiny holes
Recommended article: Homogenization limit for the diffusion equation with nonlinear flux condition on the boundary of very thin holes periodically distributed in a domain, in case of a critical size
Recommended article: Homogenization problem in a domain perforated by tiny isoperimetric holes with nonlinear Robin type boundary conditions
Recommended article: Q4385856
Recommended article: Asymptotics of solutions of boundary value problems in periodically perforated domains with small holes
description: scientific article; zbMATH DE number 4030057