TY - JOUR

T1 - Homogenization of the Neumann problem for higher order elliptic equations with periodic coefficients

AU - Суслина, Татьяна Александровна

N1 - Funding Information: This work was supported by Russian Science Foundation [grant number 17-11-01069].

PY - 2018/8/3

Y1 - 2018/8/3

N2 - Let O ⸦ R d be a bounded domain of class C 2p. In L 2(O; C n), we study a self-adjoint strongly elliptic operator A N,ε of order 2p given by the expression b(D) *g(x/ε)b(D), ε > 0, with Neumann boundary conditions. Here, g(x) is a bounded and positive definite matrix-valued function in R d, periodic with respect to some lattice; b(D) = Σ|α|=p bαDα is a differential operator of order p. The symbol b(ξ) is subject to some condition ensuring strong ellipticity of the operator A N,ε. We find approximations for the resolvent (A N,ε − ζ I) −1 in different operator norms with error estimates depending on ε and ζ.

AB - Let O ⸦ R d be a bounded domain of class C 2p. In L 2(O; C n), we study a self-adjoint strongly elliptic operator A N,ε of order 2p given by the expression b(D) *g(x/ε)b(D), ε > 0, with Neumann boundary conditions. Here, g(x) is a bounded and positive definite matrix-valued function in R d, periodic with respect to some lattice; b(D) = Σ|α|=p bαDα is a differential operator of order p. The symbol b(ξ) is subject to some condition ensuring strong ellipticity of the operator A N,ε. We find approximations for the resolvent (A N,ε − ζ I) −1 in different operator norms with error estimates depending on ε and ζ.

KW - higher order elliptic equations

KW - homogenization

KW - Neumann problem

KW - operator error estimates

KW - Periodic differential operators

UR - http://www.scopus.com/inward/record.url?scp=85028527072&partnerID=8YFLogxK

U2 - 10.1080/17476933.2017.1365845

DO - 10.1080/17476933.2017.1365845

M3 - Article

VL - 63

SP - 1185

EP - 1215

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 7-8

ER -