Quantitative estimates in stochastic homogenization for correlated coefficient fields

DOI10.2140/apde.2021.14.2497zbMath1485.35156arXiv1910.05530OpenAlexW2980091118WikidataQ114045441 ScholiaQ114045441MaRDI QIDQ2116215

Felix Otto, Stefan Neukamm, Antoine Gloria

Publication date: 16 March 2022

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.05530

zbMATH Keywords

stochastic coefficientshomogenization of linear elliptic operators

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Second-order elliptic equations (35J15) Homogenization in equilibrium problems of solid mechanics (74Q05) Second-order elliptic systems (35J47)

Related Items

Eigenvalue fluctuations for random elliptic operators in homogenization regime, Scaling limit of the homogenization commutator for Gaussian coefficient fields, Quantitative homogenization theory for random suspensions in steady Stokes flow, The structure of fluctuations in stochastic homogenization, On the Periodic Homogenization of Elliptic Equations in Nondivergence Form with Large Drifts, Optimal decay of the parabolic semigroup in stochastic homogenization for correlated coefficient fields, Working session: Quantitative stochastic homogenization. Abstracts from the working session held October 16--22, 2022, Non-perturbative approach to the Bourgain-Spencer conjecture in stochastic homogenization, A spectral ansatz for the long-time homogenization of the wave equation, Locality properties of standard homogenization commutator, Quantitative nonlinear homogenization: control of oscillations, Homogenization for operators with arbitrary perturbations in coefficients, Enhancement of elasto-dielectrics by homogenization of active charges, Multiscale functional inequalities in probability: Concentration properties, A remark on a surprising result by Bourgain in homogenization

Cites Work

• Unnamed Item
• Annealed estimates on the Green functions and uncertainty quantification
• Mesoscopic higher regularity and subadditivity in elliptic homogenization
• Random homogenization and convergence to integrals with respect to the Rosenblatt process
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• Variance decay for functionals of the environment viewed by the particle
• A regularity theory for random elliptic operators
• Annealed estimates on the Green function
• On homogenization of elliptic equations with random coefficients
• Quantitative results on the corrector equation in stochastic homogenization
• Spectral measure and approximation of homogenized coefficients
• Sublinear growth of the corrector in stochastic homogenization: optimal stochastic estimates for slowly decaying correlations
• Robustness of the pathwise structure of fluctuations in stochastic homogenization
• Multiscale functional inequalities in probability: constructive approach
• Higher-order pathwise theory of fluctuations in stochastic homogenization
• Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
• The additive structure of elliptic homogenization
• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• Quantitative
• 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
• Random integrals and correctors in homogenization
• Compactness methods in the theory of homogenization
• Convergence of integrated processes of arbitrary Hermite rank
• Quantitative Stochastic Homogenization and Large-Scale Regularity
• Quantitative estimates on the periodic approximation of the corrector in stochastic homogenization