Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?

DOI10.1051/cocv:2002046zbMath1073.35020OpenAlexW2141755871MaRDI QIDQ4421101

Patrizia Donato, Alain Damlamian

Publication date: 19 August 2003

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=COCV_2002__8__555_0

zbMATH Keywords

Sobolev spacesPoincaré-Wirtinger inequalityJones domainsNeumann type problems\(H^0\)-convergence

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (12)

Asymptotic analysis of a semi-linear elliptic system in perforated domains: well-posedness and correctors for the homogenization limit ⋮ From a microscopic to a macroscopic model for Alzheimer disease: two-scale homogenization of the Smoluchowski equation in perforated domains ⋮ Homogenization of the demagnetization field operator in periodically perforated domains ⋮ HOMOGENIZATION OF TWO HEAT CONDUCTORS WITH AN INTERFACIAL CONTACT RESISTANCE ⋮ Homogenization of the discrete diffusive coagulation-fragmentation equations in perforated domains ⋮ Unnamed Item ⋮ Homogenization results for a Landau–Lifshitz–Gilbert equation in composite materials with transmission defects ⋮ Smoluchowski Equation with Variable Coefficients in Perforated Domains: Homogenization and Applications to Mathematical Models in Medicine ⋮ A general homogenization result of spectral problem for linearized elasticity in perforated domains. ⋮ The periodic unfolding method for perforated domains and Neumann sieve models ⋮ Neumann problem for a quasilinear elliptic equation in a varying domain ⋮ Homogenization of the Poisson equation in a non-periodically perforated domain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasiextremal distance domains and extension of quasiconformal mappings
• Uniform domains
• Homogenization in open sets with holes
• Non-homogeneous media and vibration theory
• Uniform domains and the quasi-hyperbolic metric
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• The trace to the boundary of Sobolev spaces on a snowflake
• On the existence of a solution in a domain identification problem
• Homogenization of reticulated structures
• Sobolev-Poincaré implies John
• Holder Domains and Poincare Domains
• Non-homogeneous Neumann problems in domains with small holes
• THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE SECOND BOUNDARY VALUE PROBLEM UNDER FRAGMENTATION OF THE BOUNDARY OF THE DOMAIN
• Definitions for uniform domains
• Homogenization with Small Perforations of Increasingly Complicated Shapes
• An extension theorem from connected sets, and homogenization in general periodic domains
• Injectivity theorems in plane and space
• Connectedness and homogenization. Examples of fractal conductivity

This page was built for publication: Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?