Lipschitz Estimates in Almost-Periodic Homogenization

DOI10.1002/cpa.21616zbMath1367.35075arXiv1409.2094OpenAlexW1937862871MaRDI QIDQ2831148

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Publication date: 2 November 2016

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.2094

zbMATH Keywords

almost-periodic coefficientsboundary estimatessecond order elliptic problems

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Boundary value problems for second-order elliptic systems (35J57)

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Cites Work

• Unnamed Item
• Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems
• Uniform \(W^{1,p}\) estimates for systems of linear elasticity in a periodic medium
• Convergence rates in \(L ^{2}\) for elliptic homogenization problems
• \(W^{1,p}\) estimates for elliptic problems with Neumann boundary conditions in Lipschitz domains
• Boundary value problems for the systems of elastostatics in Lipschitz domains
• Homogenization of elliptic problems with \(L^p\) boundary data
• Area integral estimates for higher order elliptic equations and systems
• Bounds of Riesz transforms on \(L^p\) spaces for second order elliptic operators.
• The Dirichlet problem for the Stokes system on Lipschitz domains
• The \(L^{p}\) boundary value problems on Lipschitz domains
• Quantitative
• An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
• Uniform regularity estimates in parabolic homogenization
• W$^{1,p}$ estimates for elliptic homogenization problems in nonsmooth domains
• Compactness methods in the theory of homogenization
• AVERAGING DIFFERENTIAL OPERATORS WITH ALMOST PERIODIC, RAPIDLY OSCILLATING COEFFICIENTS
• L^p bounds on singular integrals in homogenization
• Homogenization of elliptic systems with Neumann boundary conditions

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