On homogenization for piecewise locally periodic operators

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

In: Russian Journal of Mathematical Physics, Vol. 30, No. 2, 01.06.2023, p. 270-274.

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

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