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

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Homogenization of the Dirichlet problem for higher-order elliptic equations with periodic coefficients. / Суслина, Татьяна Александровна.

в: St. Petersburg Mathematical Journal, Том 29, № 2, 2018, стр. 325-362.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{d075c0be41284299a886734954283773,

title = "Homogenization of the Dirichlet problem for higher-order elliptic equations with periodic coefficients",

abstract = "Let O ⊂ ℝ d be a bounded domain of class C 2p. The object under study is a selfadjoint strongly elliptic operator AD, e of order 2p, p ≤ 2, in L 2(O, n), given by the expression b(D)* g(x/ε)b(D), ε > 0, with the Dirichlet boundary conditions. Here g(x) is a bounded and positive definite (m×m)-matrix-valued function in ℝ d, periodic with respect to some lattice; b(D) = ∑ |α| = p bαD α is a differential operator of order p with constant coefficients; and the ba are constant (m × n)-matrices. It is assumed that m ≤ n and the symbol b(Ξ) has maximal rank. Approximations are found for the resolvent (A D,ε - ζI) -1 in the L 2(O; n)-operator norm and in the norm of operators acting from L 2(O; n) to H p(O; n), with error estimates depending on ε and ζ. ",

keywords = "Corrector, Dirichlet problem, Effective operator, Higher-order elliptic equations, Homogenization, Operator error estimates, Periodic differential operators",

author = "Суслина, {Татьяна Александровна}",

year = "2018",

doi = "10.1090/spmj/1496",

language = "English",

volume = "29",

pages = "325--362",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "2",

}

RIS

TY - JOUR

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

AU - Суслина, Татьяна Александровна

PY - 2018

Y1 - 2018

N2 - Let O ⊂ ℝ d be a bounded domain of class C 2p. The object under study is a selfadjoint strongly elliptic operator AD, e of order 2p, p ≤ 2, in L 2(O, n), given by the expression b(D)* g(x/ε)b(D), ε > 0, with the Dirichlet boundary conditions. Here g(x) is a bounded and positive definite (m×m)-matrix-valued function in ℝ d, periodic with respect to some lattice; b(D) = ∑ |α| = p bαD α is a differential operator of order p with constant coefficients; and the ba are constant (m × n)-matrices. It is assumed that m ≤ n and the symbol b(Ξ) has maximal rank. Approximations are found for the resolvent (A D,ε - ζI) -1 in the L 2(O; n)-operator norm and in the norm of operators acting from L 2(O; n) to H p(O; n), with error estimates depending on ε and ζ.

AB - Let O ⊂ ℝ d be a bounded domain of class C 2p. The object under study is a selfadjoint strongly elliptic operator AD, e of order 2p, p ≤ 2, in L 2(O, n), given by the expression b(D)* g(x/ε)b(D), ε > 0, with the Dirichlet boundary conditions. Here g(x) is a bounded and positive definite (m×m)-matrix-valued function in ℝ d, periodic with respect to some lattice; b(D) = ∑ |α| = p bαD α is a differential operator of order p with constant coefficients; and the ba are constant (m × n)-matrices. It is assumed that m ≤ n and the symbol b(Ξ) has maximal rank. Approximations are found for the resolvent (A D,ε - ζI) -1 in the L 2(O; n)-operator norm and in the norm of operators acting from L 2(O; n) to H p(O; n), with error estimates depending on ε and ζ.

KW - Corrector

KW - Dirichlet problem

KW - Effective operator

KW - Higher-order elliptic equations

KW - Homogenization

KW - Operator error estimates

KW - Periodic differential operators

UR - http://www.scopus.com/inward/record.url?scp=85043502666&partnerID=8YFLogxK

U2 - 10.1090/spmj/1496

DO - 10.1090/spmj/1496

M3 - Article

VL - 29

SP - 325

EP - 362

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 35182531