On uniform estimates for Laplace equation in balls with small holes

DOI10.1007/s00526-016-1055-yzbMath1356.35102arXiv1503.01103OpenAlexW1595674286WikidataQ115387326 ScholiaQ115387326MaRDI QIDQ342952

Yong Lu

Publication date: 18 November 2016

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.01103

zbMATH Keywords

rescalingDirichlet boundary conditionGreen functionelliptic problem\(L^p\)-estimateuniform gradient estimate

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Green's functions for elliptic equations (35J08)

Related Items

Homogenization of Stationary Navier-Stokes Equations in Domains with 3 Kinds of Typical Holes ⋮ Homogenization of Stokes equations in perforated domains: a unified approach ⋮ Uniform estimates for Stokes equations in a domain with a small hole and applications in homogenization problems ⋮ Limits of the Stokes and Navier–Stokes equations in a punctured periodic domain ⋮ Homogenization of the compressible Navier-Stokes equations in domains with very tiny holes

Cites Work

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• The inhomogeneous Dirichlet problem in Lipschitz domains
• Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I: Abstract framework, a volume distribution of holes
• 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
• Homogenization of the compressible Navier–Stokes equations in a porous medium
• Estimates for the Stokes operator in Lipschitz domains

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