Homogenization of the fourth-order elliptic operator with periodic coefficients with correctors taken into account

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Homogenization of the fourth-order elliptic operator with periodic coefficients with correctors taken into account. / Sloushch, V. A. ; Suslina, T. A. .

в: Functional Analysis and its Applications, Том 54, № 3, 2020, стр. 224-228.

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

BibTeX

@article{4f8e489acbc844d98dea23179cc2379a,

title = "Homogenization of the fourth-order elliptic operator with periodic coefficients with correctors taken into account",

abstract = "An elliptic fourth-order differential operator Aε on L2(Rd;Cn) is studied. Here ε>0 is a small parameter. It is assumed that the operator is given in the factorized form Aε=b(D)∗g(x/ε)b(D), where g(x) is a Hermitian matrix-valued function periodic with respect to some lattice and b(D) is a matrix second-order differential operator. We make assumptions ensuring that the operator Aε is strongly elliptic. The following approximation for the resolvent (Aε+I)−1 in the operator norm of L2(Rd;Cn) is obtained: (Aε+I)−1=(A0+I)−1+εK1+ε2K2(ε)+O(ε3). Here A0 is the effective operator with constant coefficients and K1 and K2(ε) are certain correctors.",

keywords = "periodic differential operators, homogenization, operator error estimates, effective operator, corrector",

author = "Sloushch, {V. A.} and Suslina, {T. A.}",

note = "Sloushch, V.A., Suslina, T.A. Homogenization of the Fourth-Order Elliptic Operator with Periodic Coefficients with Correctors Taken into Account. Funct Anal Its Appl 54, 224–228 (2020). https://doi.org/10.1134/S0016266320030077",

year = "2020",

language = "English",

volume = "54",

pages = "224--228",

journal = "Functional Analysis and its Applications",

issn = "0016-2663",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Homogenization of the fourth-order elliptic operator with periodic coefficients with correctors taken into account

AU - Sloushch, V. A.

AU - Suslina, T. A.

N1 - Sloushch, V.A., Suslina, T.A. Homogenization of the Fourth-Order Elliptic Operator with Periodic Coefficients with Correctors Taken into Account. Funct Anal Its Appl 54, 224–228 (2020). https://doi.org/10.1134/S0016266320030077

PY - 2020

Y1 - 2020

N2 - An elliptic fourth-order differential operator Aε on L2(Rd;Cn) is studied. Here ε>0 is a small parameter. It is assumed that the operator is given in the factorized form Aε=b(D)∗g(x/ε)b(D), where g(x) is a Hermitian matrix-valued function periodic with respect to some lattice and b(D) is a matrix second-order differential operator. We make assumptions ensuring that the operator Aε is strongly elliptic. The following approximation for the resolvent (Aε+I)−1 in the operator norm of L2(Rd;Cn) is obtained: (Aε+I)−1=(A0+I)−1+εK1+ε2K2(ε)+O(ε3). Here A0 is the effective operator with constant coefficients and K1 and K2(ε) are certain correctors.

AB - An elliptic fourth-order differential operator Aε on L2(Rd;Cn) is studied. Here ε>0 is a small parameter. It is assumed that the operator is given in the factorized form Aε=b(D)∗g(x/ε)b(D), where g(x) is a Hermitian matrix-valued function periodic with respect to some lattice and b(D) is a matrix second-order differential operator. We make assumptions ensuring that the operator Aε is strongly elliptic. The following approximation for the resolvent (Aε+I)−1 in the operator norm of L2(Rd;Cn) is obtained: (Aε+I)−1=(A0+I)−1+εK1+ε2K2(ε)+O(ε3). Here A0 is the effective operator with constant coefficients and K1 and K2(ε) are certain correctors.

KW - periodic differential operators

KW - homogenization

KW - operator error estimates

KW - effective operator

KW - corrector

UR - https://link.springer.com/article/10.1134/S0016266320030077

M3 - Article

VL - 54

SP - 224

EP - 228

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 3

ER -

ID: 73142091