Uniform Estimates for Dirichlet Problems in Perforated Domains

Zhongwei Shen

doi:10.1007/s10013-023-00613-7

Uniform Estimates for Dirichlet Problems in Perforated Domains

Zhongwei Shen

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

4 Scopus citations

Abstract

This paper studies the Dirichlet problem for Laplace’s equation in a domain Ω_ε_,_η perforated with small holes, where ε represents the scale of the minimal distances between holes and η the ratio between the scale of sizes of holes and ε . We establish W¹^,^p estimates for solutions with bounding constants depending explicitly on the small parameters ε and η . We also show that these estimates are either optimal or near optimal.

Original language	English
Pages (from-to)	845-867
Number of pages	23
Journal	Vietnam Journal of Mathematics
Volume	51
Issue number	4
DOIs	https://doi.org/10.1007/s10013-023-00613-7
State	Published - Oct 2023

Bibliographical note

Publisher Copyright:
© 2023, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd.

Funding

Supported in part by NSF grants DMS-1856235, DMS-2153585, and by Simons Fellowship. The author thanks the anonymous referees for helpful comments and corrections.

Funders	Funder number
National Science Foundation Arctic Social Science Program	DMS-2153585, 1856235, DMS-1856235

Keywords

Homogenization
Laplace’s equation
Perforated domain
W, estimate

ASJC Scopus subject areas

General Mathematics

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10.1007/s10013-023-00613-7

Cite this

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AB - This paper studies the Dirichlet problem for Laplace’s equation in a domain Ωε,η perforated with small holes, where ε represents the scale of the minimal distances between holes and η the ratio between the scale of sizes of holes and ε . We establish W1,p estimates for solutions with bounding constants depending explicitly on the small parameters ε and η . We also show that these estimates are either optimal or near optimal.

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KW - Laplace’s equation

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KW - W, estimate

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Uniform Estimates for Dirichlet Problems in Perforated Domains

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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