Standard

On homogenization for non-self-adjoint locally periodic elliptic operators. / Senik, N. N.

In: Functional Analysis and its Applications, Vol. 51, No. 2, 2017, p. 152-156.

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

Harvard

Senik, NN 2017, 'On homogenization for non-self-adjoint locally periodic elliptic operators', Functional Analysis and its Applications, vol. 51, no. 2, pp. 152-156. https://doi.org/10.1007/s10688-017-0178-z

APA

Senik, N. N. (2017). On homogenization for non-self-adjoint locally periodic elliptic operators. Functional Analysis and its Applications, 51(2), 152-156. https://doi.org/10.1007/s10688-017-0178-z

Vancouver

Senik NN. On homogenization for non-self-adjoint locally periodic elliptic operators. Functional Analysis and its Applications. 2017;51(2):152-156. https://doi.org/10.1007/s10688-017-0178-z

Author

Senik, N. N. / On homogenization for non-self-adjoint locally periodic elliptic operators. In: Functional Analysis and its Applications. 2017 ; Vol. 51, No. 2. pp. 152-156.

BibTeX

@article{dbf4cee8ac2c44f5ac45b3b00ac173f8,
title = "On homogenization for non-self-adjoint locally periodic elliptic operators",
abstract = "In this note we consider the homogenization problem for a matrix locally periodic elliptic operator on Rd of the form Aε = −divA(x, x/ε)∇. The function A is assumed to be H{\"o}lder continuous with exponent s ∈ [0, 1] in the “slow” variable and bounded in the “fast” variable. We construct approximations for (Aε − μ)−1, including one with a corrector, and for (−Δ)s/2(Aε − μ)−1 in the operator norm on L2(Rd)n. For s ≠ 0, we also give estimates of the rates of approximation.",
keywords = "теория усреднения, операторные оценки погрешности, локально периодические операторы, эффективный оператор, корректор",
author = "Senik, {N. N.}",
year = "2017",
doi = "10.1007/s10688-017-0178-z",
language = "English",
volume = "51",
pages = "152--156",
journal = "Functional Analysis and its Applications",
issn = "0016-2663",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - On homogenization for non-self-adjoint locally periodic elliptic operators

AU - Senik, N. N.

PY - 2017

Y1 - 2017

N2 - In this note we consider the homogenization problem for a matrix locally periodic elliptic operator on Rd of the form Aε = −divA(x, x/ε)∇. The function A is assumed to be Hölder continuous with exponent s ∈ [0, 1] in the “slow” variable and bounded in the “fast” variable. We construct approximations for (Aε − μ)−1, including one with a corrector, and for (−Δ)s/2(Aε − μ)−1 in the operator norm on L2(Rd)n. For s ≠ 0, we also give estimates of the rates of approximation.

AB - In this note we consider the homogenization problem for a matrix locally periodic elliptic operator on Rd of the form Aε = −divA(x, x/ε)∇. The function A is assumed to be Hölder continuous with exponent s ∈ [0, 1] in the “slow” variable and bounded in the “fast” variable. We construct approximations for (Aε − μ)−1, including one with a corrector, and for (−Δ)s/2(Aε − μ)−1 in the operator norm on L2(Rd)n. For s ≠ 0, we also give estimates of the rates of approximation.

KW - теория усреднения

KW - операторные оценки погрешности

KW - локально периодические операторы

KW - эффективный оператор

KW - корректор

UR - http://mi.mathnet.ru/faa3457

U2 - 10.1007/s10688-017-0178-z

DO - 10.1007/s10688-017-0178-z

M3 - Article

VL - 51

SP - 152

EP - 156

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 2

ER -

ID: 7754872