Uniform W1,p estimates and large-scale regularity for Dirichlet problems in perforated domains

Zhongwei Shen; Jamison Wallace

doi:10.1016/j.jfa.2023.110118

Uniform W^1,p estimates and large-scale regularity for Dirichlet problems in perforated domains

Zhongwei Shen
, Jamison Wallace

Producción científica: Article › revisión exhaustiva

5 Citas (Scopus)

Resumen

In this paper we study the Dirichlet problem for Laplace's equation in a domain ω_ε,η perforated periodically with small holes in R^d, 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 W^1,p estimates for solutions with bounding constants depending explicitly on ε and η. The proof relies on a large-scale Lipschitz estimate for harmonic functions in perforated domains. The results are optimal for d≥2.

Idioma original	English
Número de artículo	110118
Publicación	Journal of Functional Analysis
Volumen	285
N.º	10
DOI	https://doi.org/10.1016/j.jfa.2023.110118
Estado	Published - nov 15 2023

Nota bibliográfica

Publisher Copyright:
© 2023 Elsevier Inc.

Financiación

Supported in part by NSF grants DMS-1856235, DMS-2153585, and by Simons Fellowship grant 816002.Supported in part by NSF grants DMS-1856235 and DMS-2153585.

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	DMS-2153585, 1856235, DMS-1856235, 816002

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2023.110118

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abstract = "In this paper we study the Dirichlet problem for Laplace's equation in a domain ωε,η perforated periodically with small holes in Rd, 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 ε and η. The proof relies on a large-scale Lipschitz estimate for harmonic functions in perforated domains. The results are optimal for d≥2.",

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AU - Wallace, Jamison

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N2 - In this paper we study the Dirichlet problem for Laplace's equation in a domain ωε,η perforated periodically with small holes in Rd, 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 ε and η. The proof relies on a large-scale Lipschitz estimate for harmonic functions in perforated domains. The results are optimal for d≥2.

AB - In this paper we study the Dirichlet problem for Laplace's equation in a domain ωε,η perforated periodically with small holes in Rd, 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 ε and η. The proof relies on a large-scale Lipschitz estimate for harmonic functions in perforated domains. The results are optimal for d≥2.

KW - Homogenization

KW - Large-scale regularity

KW - Perforated domain

KW - Uniform estimates

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