G-convergence of elliptic operators in nondivergence form
type: Item
instance of: scholarly article
title: G-convergence of elliptic operators in nondivergence form
zbMATH Open document ID: 0588.35033
DOI: 10.1007/BF01158181
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: In the smooth bounded domain \({\mathcal D}\) of the Euclidean space \(E_ d\) a sequence of elliptic operators \(L_ n\), \(n=1,2,...\), of the type \[ L_ n=a_ n^{ij}(x)\partial^ 2/\partial x^ i\partial x^ j+b^ i_ n(x)\partial /\partial x^ i+c_ n(x), \] is given, where \(c_ n\leq 0\), \(a_ n^{ij}\), \(b^ i_ n\), \(c_ n\) are uniformly bounded in n with respect to \({\mathcal D}\), \(a_ n^{ij}=a_ n^{ji}\) and the matrices \((a_ n^{ij})\) are non-degenerate \({\mathcal D}\) with respect to n, x. If the coefficients of \(L_ n\) are smooth in \(\bar {\mathcal D}\), then it is known, that for any function \(f\in {\mathcal L}_ p({\mathcal D})\) there exists a unique function \(u_ n\in \overset\circ W^ 2_ p({\mathcal D})\) such that \(L_ nu_ n=f\). The paper gives a positive solution of the problem to select a subsequence, which converges to some function u with \(Lu=f\), where L is a constructed elliptic operator.
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 3944382
zbMATH Keywords: G-convergence
zbMATH Keywords: sequence of elliptic operators
zbMATH Keywords: positive solution
author: N. V. Krylov
reviewed by: A. A. Martynyuk
MaRDI profile type: Publication
cites work: Q3940186
cites work: Q5513924
cites work: Harnack's inequality for elliptic equations and the Hölder property of their solutions
cites work: Q3658831
full work available at URL: https://doi.org/10.1007/bf01158181
OpenAlex ID: W2049909798
description: scientific article; zbMATH DE number 3944382