Spectral approach to homogenization of elliptic operators in a perforated space

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Spectral approach to homogenization of elliptic operators in a perforated space. / Суслина, Татьяна Александровна.

In: Reviews in Mathematical Physics, Vol. 30, No. 8, 1840016, 01.09.2018.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c0620834485e45eca17cc20efd6e86bf,

title = "Spectral approach to homogenization of elliptic operators in a perforated space",

abstract = "Let Γ ⊂ Rd be a lattice. For ϵ > 0, we consider the perforated space {"} ⊂ Rd which is an ({"}Γ)-periodic open connected set with Lipschitz boundary. In L2(IIϵ;Cn), we consider a self-adjoint strongly elliptic second-order differential operator Aϵ with periodic coefficients depending on x=ϵ. We study the behavior of the resolvent (Aϵ + I)-1 for small ϵ. Approximations for this resolvent in the (L2 → L2) and (L2 → H1)-operator norms with sharp order error estimates are found. The results are obtained by the operator-theoretic (spectral) approach. General results are applied to particular periodic operators of mathematical physics: the acoustics operator, the elasticity operator, and the Schr{\"o}dinger operator with a singular potential.",

author = "Суслина, {Татьяна Александровна}",

note = "Funding Information: The author is grateful to Nikolai Filonov and Alexander Nazarov for fruitful discussions. This work was supported by Russian Foundation for Basic Research (grant no. 16-01-00087).",

year = "2018",

month = sep,

day = "1",

doi = "10.1142/S0129055X18400160",

language = "English",

volume = "30",

journal = "Reviews in Mathematical Physics",

issn = "0129-055X",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

number = "8",

}

RIS

TY - JOUR

T1 - Spectral approach to homogenization of elliptic operators in a perforated space

AU - Суслина, Татьяна Александровна

N1 - Funding Information: The author is grateful to Nikolai Filonov and Alexander Nazarov for fruitful discussions. This work was supported by Russian Foundation for Basic Research (grant no. 16-01-00087).

PY - 2018/9/1

Y1 - 2018/9/1

N2 - Let Γ ⊂ Rd be a lattice. For ϵ > 0, we consider the perforated space " ⊂ Rd which is an ("Γ)-periodic open connected set with Lipschitz boundary. In L2(IIϵ;Cn), we consider a self-adjoint strongly elliptic second-order differential operator Aϵ with periodic coefficients depending on x=ϵ. We study the behavior of the resolvent (Aϵ + I)-1 for small ϵ. Approximations for this resolvent in the (L2 → L2) and (L2 → H1)-operator norms with sharp order error estimates are found. The results are obtained by the operator-theoretic (spectral) approach. General results are applied to particular periodic operators of mathematical physics: the acoustics operator, the elasticity operator, and the Schrödinger operator with a singular potential.

AB - Let Γ ⊂ Rd be a lattice. For ϵ > 0, we consider the perforated space " ⊂ Rd which is an ("Γ)-periodic open connected set with Lipschitz boundary. In L2(IIϵ;Cn), we consider a self-adjoint strongly elliptic second-order differential operator Aϵ with periodic coefficients depending on x=ϵ. We study the behavior of the resolvent (Aϵ + I)-1 for small ϵ. Approximations for this resolvent in the (L2 → L2) and (L2 → H1)-operator norms with sharp order error estimates are found. The results are obtained by the operator-theoretic (spectral) approach. General results are applied to particular periodic operators of mathematical physics: the acoustics operator, the elasticity operator, and the Schrödinger operator with a singular potential.

UR - http://www.scopus.com/inward/record.url?scp=85052190453&partnerID=8YFLogxK

U2 - 10.1142/S0129055X18400160

DO - 10.1142/S0129055X18400160

M3 - Article

VL - 30

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

SN - 0129-055X

IS - 8

M1 - 1840016

ER -

ID: 36231049