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

Результат исследований: Научные публикации в периодических изданияхстатьярецензирование

1 Цитирования (Scopus)

Аннотация

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.
Язык оригиналаанглийский
Страницы (с-по)224-228
ЖурналFunctional Analysis and its Applications
Том54
Номер выпуска3
СостояниеОпубликовано - 2020

Предметные области Scopus

  • Математика (все)

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