Averaging of singularly perturbed elliptic operators
type: Item
instance of: scholarly article
title: Averaging of singularly perturbed elliptic operators
zbMATH Open document ID: 0556.35003
DOI: 10.1007/BF01157062
author: E. V. Krivenko
author: V. V. Zhikov
published in: Mathematical Notes
publication date: 1983-01-01T00:00:00Z
review text: The authors consider a family of operators of the form \[ L_{\epsilon}=\epsilon^{2\ell}\sum_{| \alpha | =| \beta | =m_ 1}(-1)^{m_ 1}D^{\alpha}(a_{\alpha \beta}(\epsilon^{-1}x)D^{\beta})+\sum_{| \alpha | =| \beta | =m}(-1)^ mD^{\alpha}(a_{\alpha \beta}(\epsilon^{- 1}x)D^{\beta}), \] where \(\ell =m_ 1-m>0\), \(\epsilon >0\) is a small parameter. They determine conditions for the coefficients \(\{a_{\alpha \beta}(x)\}\) such that the family \(L_{\epsilon}\) has a strong G-limit for \(\epsilon\) \(\to 0\).
reviewed by: A. A. Martynyuk
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35J35
zbMATH DE Number: 3886361
zbMATH Keywords: strong G-limit
MaRDI profile type: Publication
cites work: Q3092574
cites work: Q4481511
full work available at URL: https://doi.org/10.1007/bf01157062
OpenAlex ID: W2088448644
description: scientific article; zbMATH DE number 3886361