Quantitative analysis of boundary layers in periodic homogenization

DOI10.1007/s00205-017-1142-zzbMath1373.35028arXiv1607.06716OpenAlexW2488772071MaRDI QIDQ1675111

Christophe Prange, Tuomo Kuusi, Jean-Christophe Mourrat, Scott N. Armstrong

Publication date: 26 October 2017

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06716

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Asymptotic expansions of solutions to PDEs (35C20) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Boundary value problems for second-order elliptic systems (35J57)

Related Items (16)

A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media ⋮ Periodic homogenization of Green's functions for Stokes systems ⋮ Working session: Quantitative stochastic homogenization. Abstracts from the working session held October 16--22, 2022 ⋮ Liouville Principles and a Large-Scale Regularity Theory for Random Elliptic Operators on the Half-Space ⋮ Stochastic Homogenization and Geometric Singularities: A Study on Corners ⋮ Asymptotic Expansion of the Spectrum for Periodic Schrödinger Operators ⋮ Homogenization of oblique boundary value problems ⋮ Neumann Homogenization via Integro-Differential Operators. Part 2: Singular Gradient Dependence ⋮ Homogenization and boundary layers in domains of finite type ⋮ Regularity of homogenized boundary data in periodic homogenization of elliptic systems ⋮ Optimal Convergence Rates for Elliptic Homogenization Problems in Nondivergence-Form: Analysis and Numerical Illustrations ⋮ Higher order convergence rates in theory of homogenization. II: Oscillatory initial data ⋮ Third-order corrections in periodic homogenization for elliptic problem ⋮ Oscillatory Integrals and Periodic Homogenization of Robin Boundary Value Problems ⋮ First-order expansions for eigenvalues and eigenfunctions in periodic homogenization ⋮ Regularity for the stationary Navier-Stokes equations over bumpy boundaries and a local wall law

Cites Work

• Unnamed Item
• Bounded correctors in almost periodic homogenization
• Applications of Fourier analysis in homogenization of Dirichlet problem. III: Polygonal domains
• Homogenization in polygonal domains
• Homogenization and boundary layers
• Estimates for Green's matrices of elliptic systems by \(L^ p\) theory
• Applications of Fourier analysis in homogenization of Dirichlet problem I. Pointwise estimates
• Homogenization of the oscillating Dirichlet boundary condition in general domains
• Convergence rates in periodic homogenization of systems of elasticity
• Compactness methods in the theory of homogenization
• L^p bounds on singular integrals in homogenization
• Boundary layer tails in periodic homogenization
• First-order corrections to the homogenised eigenvalues of a periodic composite medium. A convergence proof
• Continuity and discontinuity of the boundary layer tail
• Asymptotic Analysis of Boundary Layer Correctors in Periodic Homogenization
• Periodic Homogenization of Green and Neumann Functions

This page was built for publication: Quantitative analysis of boundary layers in periodic homogenization