An Introduction to the Qualitative and Quantitative Theory of Homogenization

DOI10.4036/iis.2018.A.01zbMath1481.35010arXiv1707.08992MaRDI QIDQ5135237

Stefan Neukamm

Publication date: 19 November 2020

Published in: Interdisciplinary Information Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08992

zbMATH Keywords

periodic homogenizationcorrectortwo-scale expansionquantitative stochastic homogenizationTartar's method of oscillating test functions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs with randomness, stochastic partial differential equations (35R60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)

Related Items

Space-time homogenization for nonlinear diffusion ⋮ <i>H</i>-Compactness of Elliptic Operators on Weighted Riemannian Manifolds ⋮ Berry-Esseen theorem and quantitative homogenization for the random conductance model with degenerate conductances ⋮ Rate of convergence for periodic homogenization of convex Hamilton–Jacobi equations in one dimension ⋮ Two-scale homogenization of abstract linear time-dependent PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Random walks on disordered media and their scaling limits. École d'Été de Probabilités de Saint-Flour XL -- 2010
• Recent progress on the random conductance model
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• A regularity theory for random elliptic operators
• Annealed estimates on the Green function
• Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
• The Green function for uniformly elliptic equations
• Parabolic Harnack inequality and estimates of Markov chains on graphs
• Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
• Berry-Esseen theorem and quantitative homogenization for the random conductance model with degenerate conductances
• The additive structure of elliptic homogenization
• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• An optimal quantitative two-scale expansion in stochastic homogenization of discrete elliptic equations
• Moment bounds on the corrector of stochastic homogenization of non-symmetric elliptic finite difference equations
• Ergodic theorems for superadditive processes.
• Multiscale functional inequalities in probability: Concentration properties
• Quantitative Stochastic Homogenization and Large-Scale Regularity