Operator estimates for elliptic problem with rapidly alternating Steklov boundary condition
type: Item
instance of: scholarly article
title: Operator estimates for elliptic problem with rapidly alternating Steklov boundary condition
zbMATH Open document ID: 1437.35517
author: A. G. Chechkina
author: Ciro D'Apice
author: Umberto De Maio
published in: Journal of Computational and Applied Mathematics
publication date: 2020-04-15T00:00:00Z
review text: The authors consider a boundary value problem for the Laplace equation with frequently alternating boundary conditions in a two-dimensional domain. The boundary of the domain is partitioned into many small pieces, on which the Dirichlet condition and Steklov inhomogeneous spectral condition are imposed in turns. The mentioned partition is quasi-periodic and the sizes of the Dirichlet and Steklov pieces of the boundary are such that in the limit, the homogenized condition is the Steklov one. The perturbed and the homogenized problem are reformulated in terms of some self-adjoint operators in a fractional Sobolev space on the boundary and the main result is the norm convergence of the mentioned self-adjoint operators. An estimate for the convergence rate is established. This result implies the convergence of the spectrum of the original perturbed problem to that of the homogenized ones as well as a similar convergence for the associated spectral projectors. The approach is based essentially on techniques from a recently submitted work by the reviewer et al.
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 7189419
zbMATH Keywords: homogenization
zbMATH Keywords: rapidly changing boundary conditions
zbMATH Keywords: Steklov-type problem
reviewed by: Denis Borisov
MaRDI profile type: Publication
full work available at URL: j.cam.2020.112802
OpenAlex ID: W3007428227
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DOI: 10.1016/J.CAM.2020.112802
description: scientific article; zbMATH DE number 7189419