Uniform estimates for Dirichlet problems in perforated domains

DOI10.1007/s10013-023-00613-7arXiv2208.12198OpenAlexW4376128285MaRDI QIDQ6185757

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Publication date: 8 January 2024

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.12198

zbMATH Keywords

Dirichlet problemLaplace equationperforated domain\(W^{1,p}\) estimates

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Cites Work

• Asymptotic expansions in perforated media with a periodic structure
• Some uniform elliptic estimates in a porous medium
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Compactness and large-scale regularity for Darcy's law
• Homogenization of Stokes equations in perforated domains: a unified approach
• Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. II: Non-critical sizes of the holes for a volume distribution and a surface distribution of holes
• A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
• A Unified Homogenization Approach for the Dirichlet Problem in Perforated Domains
• Homogenization of the Poisson equation in a non-periodically perforated domain
• Random homogenization and singular perturbations in perforated domains
• Uniform \(W^{1,p}\) estimates and large-scale regularity for Dirichlet problems in perforated domains
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