Stochastic Homogenization of Linear Elliptic Equations: Higher-Order Error Estimates in Weak Norms Via Second-Order Correctors

DOI10.1137/16M110229XzbMath1380.35011arXiv1609.01528OpenAlexW2964103479MaRDI QIDQ4594921

Felix Otto, Peter Bella, Julian Fischer, Benjamin Fehrman

Publication date: 27 November 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01528

zbMATH Keywords

optimal error estimatestwo-scale expansionsecond-order correctorsweak spatial norms

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) PDEs with randomness, stochastic partial differential equations (35R60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) Second-order elliptic systems (35J47)

Related Items (16)

Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise ⋮ Generalized slip condition over rough surfaces ⋮ Elliptic Equations with Degenerate Weights ⋮ High order correctors and two-scale expansions in stochastic homogenization ⋮ Second-Order Homogenization of Periodic Schrödinger Operators with Highly Oscillating Potentials ⋮ Non-perturbative approach to the Bourgain-Spencer conjecture in stochastic homogenization ⋮ Stochastic homogenization of Gaussian fields on random media ⋮ Time harmonic wave propagation in one dimensional weakly randomly perturbed periodic media ⋮ Higher-order pathwise theory of fluctuations in stochastic homogenization ⋮ Effective multipoles in random media ⋮ The fractional \(p\)-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps ⋮ Berry-Esseen theorem and quantitative homogenization for the random conductance model with degenerate conductances ⋮ Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems ⋮ A remark on a surprising result by Bourgain in homogenization ⋮ The choice of representative volumes in the approximation of effective properties of random materials ⋮ A regularity theory for random elliptic operators

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