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arXiv · 2502.09493

Quantitative estimates for high-contrast random media

Peter Bella·Matteo Capoferri·Mikhail Cherdantsev·Igor Velčić
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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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Peter Bella, Matteo Capoferri, Mikhail Cherdantsev, Igor Velčić. 2025-02-13. Quantitative estimates for high-contrast random media. https://arxiv.org/abs/2502.09493

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