Homogenization of boundary value problems in perforated Lipschitz domains

Zhongwei Shen

doi:10.1016/j.jde.2023.09.005

Homogenization of boundary value problems in perforated Lipschitz domains

Zhongwei Shen

Mathematics

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

Abstract

This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet, regularity, and Neumann problems with L² boundary data in a periodically perforated Lipschitz domain.

Original language	English
Pages (from-to)	283-339
Number of pages	57
Journal	Journal of Differential Equations
Volume	376
DOIs	https://doi.org/10.1016/j.jde.2023.09.005
State	Published - Dec 15 2023

Bibliographical note

Funding Information:
Supported in part by NSF grant DMS-1856235.

Publisher Copyright:
© 2023 Elsevier Inc.

Keywords

Boundary estimate
Homogenization
Perforated domain

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2023.09.005

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title = "Homogenization of boundary value problems in perforated Lipschitz domains",

abstract = "This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet, regularity, and Neumann problems with L2 boundary data in a periodically perforated Lipschitz domain.",

keywords = "Boundary estimate, Homogenization, Perforated domain",

author = "Zhongwei Shen",

note = "Funding Information: Supported in part by NSF grant DMS-1856235. Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2023",

month = dec,

day = "15",

doi = "10.1016/j.jde.2023.09.005",

language = "English",

volume = "376",

pages = "283--339",

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T1 - Homogenization of boundary value problems in perforated Lipschitz domains

AU - Shen, Zhongwei

PY - 2023/12/15

Y1 - 2023/12/15

N2 - This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet, regularity, and Neumann problems with L2 boundary data in a periodically perforated Lipschitz domain.

AB - This paper is concerned with boundary regularity estimates in the homogenization of elliptic equations with rapidly oscillating and high-contrast coefficients. We establish uniform nontangential-maximal-function estimates for the Dirichlet, regularity, and Neumann problems with L2 boundary data in a periodically perforated Lipschitz domain.

KW - Boundary estimate

KW - Homogenization

KW - Perforated domain

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UR - http://www.scopus.com/inward/citedby.url?scp=85170692295&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2023.09.005

DO - 10.1016/j.jde.2023.09.005

M3 - Article

AN - SCOPUS:85170692295

SN - 0022-0396

VL - 376

SP - 283

EP - 339

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Homogenization of boundary value problems in perforated Lipschitz domains

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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