Analyticity of homogenized coefficients under Bernoulli perturbations and the Clausius-Mossotti formulas

DOI10.1007/s00205-015-0933-3zbMath1339.35023arXiv1502.03303OpenAlexW2135256955MaRDI QIDQ261302

Mitia Duerinckx, Antoine Gloria

Publication date: 23 March 2016

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.03303

zbMATH Keywords

Clausius-Mossotti formulaecluster expansionsnon-periodic homogenisation

Mathematics Subject Classification ID

PDEs with randomness, stochastic partial differential equations (35R60) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

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Cites Work

• Annealed estimates on the Green functions and uncertainty quantification
• Random parking, Euclidean functionals, and rubber elasticity
• First-order expansion of homogenized coefficients under Bernoulli perturbations
• An optimal variance estimate in stochastic homogenization of discrete elliptic equations
• Moment bounds for the corrector in stochastic homogenization of a percolation model
• A new method of normal approximation
• Quantitative results on the corrector equation in stochastic homogenization
• New Berry-Esseen bounds for functionals of binomial point processes
• Averaging of dilute random media: a rigorous proof of the Clausius-Mossotti formula
• Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics
• An optimal error estimate in stochastic homogenization of discrete elliptic equations
• ANALYTIC REGULARITY AND POLYNOMIAL APPROXIMATION OF PARAMETRIC AND STOCHASTIC ELLIPTIC PDE'S
• A Numerical Approach Related to Defect-Type Theories for Some Weakly Random Problems in Homogenization
• The determination of the elastic field of an ellipsoidal inclusion, and related problems
• On annealed elliptic Green function estimates
• Elements of Mathematical Foundations for Numerical Approaches for Weakly Random Homogenization Problems
• The Clausius--Mossotti Formula in a Dilute Random Medium with Fixed Volume Fraction
• A Control Variate Approach Based on a Defect-Type Theory for Variance Reduction in Stochastic Homogenization
• Random parking, sequential adsorption, and the jamming limit
• Random heterogeneous materials. Microstructure and macroscopic properties
• Reduction in the resonance error in numerical homogenization. II: Correctors and extrapolation

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