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On homogenization for piecewise locally periodic operators. / Сеник, Никита Николаевич.

в: Russian Journal of Mathematical Physics, Том 30, № 2, 01.06.2023, стр. 270-274.

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Harvard

Сеник, НН 2023, 'On homogenization for piecewise locally periodic operators', Russian Journal of Mathematical Physics, Том. 30, № 2, стр. 270-274. https://doi.org/10.1134/s1061920823020139

APA

Сеник, Н. Н. (2023). On homogenization for piecewise locally periodic operators. Russian Journal of Mathematical Physics, 30(2), 270-274. https://doi.org/10.1134/s1061920823020139

Vancouver

Сеник НН. On homogenization for piecewise locally periodic operators. Russian Journal of Mathematical Physics. 2023 Июнь 1;30(2):270-274. https://doi.org/10.1134/s1061920823020139

Author

Сеник, Никита Николаевич. / On homogenization for piecewise locally periodic operators. в: Russian Journal of Mathematical Physics. 2023 ; Том 30, № 2. стр. 270-274.

BibTeX

@article{2c9dc19e5ebf44c29cc96c83303ef9db,
title = "On homogenization for piecewise locally periodic operators",
abstract = "Abstract: We discuss homogenization of a strongly elliptic operator (Formula Presented.) on a bounded C1,1 domain in Rd with either Dirichlet or Neumann boundary condition. The function A is piecewise Lipschitz in the first variable and periodic in the second one, and the function (Formula Presented.) is identically equal to (Formula Presented.) on each piece (Formula Presented.) , with (Formula Presented.) . For μ in a resolvent set, we show that the resolvent (Formula Presented.) , in the operator norm on (Formula Presented.) to the resolvent (Formula Presented.) of the effective operator at the rate (fFormula Presented.) , where (Formula Presented.) stands for the largest of (Formula Presented.) . We also obtain an approximation for the resolvent in the operator norm from (Formula Presented.) with error of order (Formula Presented.) .",
author = "Сеник, {Никита Николаевич}",
year = "2023",
month = jun,
day = "1",
doi = "10.1134/s1061920823020139",
language = "English",
volume = "30",
pages = "270--274",
journal = "Russian Journal of Mathematical Physics",
issn = "1061-9208",
publisher = "МАИК {"}Наука/Интерпериодика{"}",
number = "2",

}

RIS

TY - JOUR

T1 - On homogenization for piecewise locally periodic operators

AU - Сеник, Никита Николаевич

PY - 2023/6/1

Y1 - 2023/6/1

N2 - Abstract: We discuss homogenization of a strongly elliptic operator (Formula Presented.) on a bounded C1,1 domain in Rd with either Dirichlet or Neumann boundary condition. The function A is piecewise Lipschitz in the first variable and periodic in the second one, and the function (Formula Presented.) is identically equal to (Formula Presented.) on each piece (Formula Presented.) , with (Formula Presented.) . For μ in a resolvent set, we show that the resolvent (Formula Presented.) , in the operator norm on (Formula Presented.) to the resolvent (Formula Presented.) of the effective operator at the rate (fFormula Presented.) , where (Formula Presented.) stands for the largest of (Formula Presented.) . We also obtain an approximation for the resolvent in the operator norm from (Formula Presented.) with error of order (Formula Presented.) .

AB - Abstract: We discuss homogenization of a strongly elliptic operator (Formula Presented.) on a bounded C1,1 domain in Rd with either Dirichlet or Neumann boundary condition. The function A is piecewise Lipschitz in the first variable and periodic in the second one, and the function (Formula Presented.) is identically equal to (Formula Presented.) on each piece (Formula Presented.) , with (Formula Presented.) . For μ in a resolvent set, we show that the resolvent (Formula Presented.) , in the operator norm on (Formula Presented.) to the resolvent (Formula Presented.) of the effective operator at the rate (fFormula Presented.) , where (Formula Presented.) stands for the largest of (Formula Presented.) . We also obtain an approximation for the resolvent in the operator norm from (Formula Presented.) with error of order (Formula Presented.) .

UR - https://www.mendeley.com/catalogue/6d93a68e-dde4-316e-bd8f-ad716c56bd5d/

U2 - 10.1134/s1061920823020139

DO - 10.1134/s1061920823020139

M3 - Article

VL - 30

SP - 270

EP - 274

JO - Russian Journal of Mathematical Physics

JF - Russian Journal of Mathematical Physics

SN - 1061-9208

IS - 2

ER -

ID: 105615615