Applications of Fourier analysis in homogenization of Dirichlet problem. III: Polygonal domains

DOI10.1007/s00041-014-9327-4zbMath1331.35030arXiv1307.4999OpenAlexW2593787743MaRDI QIDQ485247

Hayk Aleksanyan, Henrik Shahgholian, Per Sjoelin

Publication date: 9 January 2015

Published in: Archive for Rational Mechanics and Analysis, The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.4999

zbMATH Keywords

Dirichlet problemhomogenizationFourier analysisconvergence ratepolygonal domainelliptic equations in divergence formDiophantine conditionrapidly oscillating boundary data

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) 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 (18)

\(L^{2}\)-estimates for singular oscillatory integral operators ⋮ Regularity of boundary data in periodic homogenization of elliptic systems in layered media ⋮ Quantitative analysis of boundary layers in periodic homogenization ⋮ Continuity and discontinuity of the boundary layer tail ⋮ Liouville Principles and a Large-Scale Regularity Theory for Random Elliptic Operators on the Half-Space ⋮ Homogenization for both oscillating operator and Neumann boundary value: \(W^{1, p}\) convergence rate ⋮ Homogenization for operators with arbitrary perturbations in coefficients ⋮ Homogenization and boundary layers in domains of finite type ⋮ Regularity of homogenized boundary data in periodic homogenization of elliptic systems ⋮ Applications of Fourier analysis in homogenization of Dirichlet problem. III: Polygonal domains ⋮ Optimal Convergence Rates for Elliptic Homogenization Problems in Nondivergence-Form: Analysis and Numerical Illustrations ⋮ Oscillatory Integrals and Periodic Homogenization of Robin Boundary Value Problems ⋮ Slow Convergence in Periodic Homogenization Problems for Divergence-Type Elliptic Operators ⋮ Homogenization of Steklov eigenvalues with rapidly oscillating weights ⋮ Homogenization of nonlinear equations with mixed boundary conditions ⋮ Sharp convergence rates for Darcy’s law ⋮ Convergence rates of nonlinear Stokes problems in homogenization ⋮ Convergence rates in homogenization of \(p\)-Laplace equations

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