TY - JOUR

T1 - Homogenization for locally periodic elliptic operators

AU - Senik, Nikita N.

N1 - Publisher Copyright: © 2021 Elsevier Inc.

PY - 2022/1/15

Y1 - 2022/1/15

N2 - We study the homogenization problem for matrix strongly elliptic operators on L-2(R-d)(n) of the form A(epsilon) = - div A(x , x/epsilon)del. The function A is Lipschitz in the first variable and periodic in the second. We do not require that A* = A, so A(epsilon) need not be self-adjoint. In this paper we provide the first two terms of a uniform approximation for (A(epsilon) - mu)(-1) and the first term of a uniform approximation for del(A(epsilon) - mu)(-1) as epsilon -> 0. Primary attention is paid to proving sharp-order bounds on the errors of approximation. (C) 2021 Elsevier Inc. All rights reserved.

AB - We study the homogenization problem for matrix strongly elliptic operators on L-2(R-d)(n) of the form A(epsilon) = - div A(x , x/epsilon)del. The function A is Lipschitz in the first variable and periodic in the second. We do not require that A* = A, so A(epsilon) need not be self-adjoint. In this paper we provide the first two terms of a uniform approximation for (A(epsilon) - mu)(-1) and the first term of a uniform approximation for del(A(epsilon) - mu)(-1) as epsilon -> 0. Primary attention is paid to proving sharp-order bounds on the errors of approximation. (C) 2021 Elsevier Inc. All rights reserved.

KW - Corrector

KW - Effective operator

KW - Homogenization

KW - Locally periodic operators

KW - Operator error estimates

KW - ERROR ESTIMATE

KW - SYSTEMS

UR - http://www.scopus.com/inward/record.url?scp=85113672483&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/76a1a55a-f4e1-368c-bbdd-ca7b4f334d92/

U2 - 10.1016/j.jmaa.2021.125581

DO - 10.1016/j.jmaa.2021.125581

M3 - Article

AN - SCOPUS:85113672483

VL - 505

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

M1 - 125581

ER -