Uniform Regularity for Degenerate Elliptic Equations in Perforated Domains

Zhongwei Shen; Jinping Zhuge

doi:10.1007/s10114-025-3640-5

Uniform Regularity for Degenerate Elliptic Equations in Perforated Domains

Zhongwei Shen
, Jinping Zhuge

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

2 Scopus citations

Abstract

This paper is concerned with a class of degenerate elliptic equations with rapidly oscillating coefficients in periodically perforated domains, which arises in the study of spectrum problems for uniformly elliptic equations in perforated domains. We establish a quantitative convergence rate and obtain the uniform weighted Lipschitz and W^1,p estimates.

Original language	English
Pages (from-to)	378-412
Number of pages	35
Journal	Acta Mathematica Sinica, English Series
Volume	41
Issue number	1
DOIs	https://doi.org/10.1007/s10114-025-3640-5
State	Published - Jan 2025

Bibliographical note

Publisher Copyright:
© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2025.

Funding

The first author is supported by NSF (Grant No. DMS-2153585), the second author is supported NSFC Grant for Excellent Youth from the NSFC and AMSS-CAS Acknowledgements

Funders	Funder number
National Natural Science Foundation of China (NSFC)
AMSS-CAS
National Science Foundation Arctic Social Science Program	DMS-2153585

Keywords

35B27
35J70
Homogenization
perforated domains
uniform regularity

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1007/s10114-025-3640-5

Cite this

@article{c10e165b1e4e4bdcadfa4c62f571e429,

title = "Uniform Regularity for Degenerate Elliptic Equations in Perforated Domains",

abstract = "This paper is concerned with a class of degenerate elliptic equations with rapidly oscillating coefficients in periodically perforated domains, which arises in the study of spectrum problems for uniformly elliptic equations in perforated domains. We establish a quantitative convergence rate and obtain the uniform weighted Lipschitz and W1,p estimates.",

keywords = "35B27, 35J70, Homogenization, perforated domains, uniform regularity",

author = "Zhongwei Shen and Jinping Zhuge",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag GmbH Germany \& The Editorial Office of AMS 2025.",

year = "2025",

month = jan,

doi = "10.1007/s10114-025-3640-5",

language = "English",

volume = "41",

pages = "378--412",

number = "1",

}

TY - JOUR

T1 - Uniform Regularity for Degenerate Elliptic Equations in Perforated Domains

AU - Shen, Zhongwei

AU - Zhuge, Jinping

N1 - Publisher Copyright: © Springer-Verlag GmbH Germany & The Editorial Office of AMS 2025.

PY - 2025/1

Y1 - 2025/1

N2 - This paper is concerned with a class of degenerate elliptic equations with rapidly oscillating coefficients in periodically perforated domains, which arises in the study of spectrum problems for uniformly elliptic equations in perforated domains. We establish a quantitative convergence rate and obtain the uniform weighted Lipschitz and W1,p estimates.

AB - This paper is concerned with a class of degenerate elliptic equations with rapidly oscillating coefficients in periodically perforated domains, which arises in the study of spectrum problems for uniformly elliptic equations in perforated domains. We establish a quantitative convergence rate and obtain the uniform weighted Lipschitz and W1,p estimates.

KW - 35B27

KW - 35J70

KW - Homogenization

KW - perforated domains

KW - uniform regularity

UR - https://www.scopus.com/pages/publications/85218087877

UR - https://www.scopus.com/pages/publications/85218087877#tab=citedBy

U2 - 10.1007/s10114-025-3640-5

DO - 10.1007/s10114-025-3640-5

M3 - Article

AN - SCOPUS:85218087877

SN - 1439-8516

VL - 41

SP - 378

EP - 412

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 1

ER -

Uniform Regularity for Degenerate Elliptic Equations in Perforated Domains

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this