Quantitative estimates for high-contrast random media

2025/02/13 by Bella, Peter, Capoferri, Matteo, Cherdantsev, Mikhail +1 · 1 citation
#35B40 #35J70 #60H25 (primary) 35B27 #74A40 #74Q05 (secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2502.09493

Abstract

This paper studies quantitative homogenization of elliptic equations with random, uniformly elliptic coefficients that vanish in a union of random holes. Assuming an upper bound on the size of the holes and a separation condition between them, we derive optimal bounds for the regularity radius r_* and suboptimal growth estimates for the corrector. These results are key ingredients for error analysis in stochastic homogenization and serve as crucial input for recent developments in the double-porosity model, such as those by Bonhomme, Duerinckx, and Gloria (arXiv:2502.02847).

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• Anderson localization in high-contrast media with random spherical inclusions

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