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Homogenization of the stochastic double-porosity model

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arxiv 2502.02847 v2 pith:DVVXML2L submitted 2025-02-05 math.AP math.PR

Elise Bonhomme , Mitia Duerinckx , Antoine Gloria This is my paper · ORCID
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keywords homogenizationdouble-porosityresonantstochasticunderassumptionsboundedcase
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This work is devoted to the homogenization of elliptic equations in high-contrast media in the so-called 'double-porosity' resonant regime, for which we solve two open problems of the literature. First, we prove qualitative stochastic homogenization under very weak conditions, which cover the case of inclusions that are not uniformly bounded or separated. Second, under stronger assumptions, we provide sharp error estimates for the two-scale expansion. The main difficulty is related to the loss of integrability of the control in the resonant zones.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Homogenisation and spectral convergence of high-contrast convolution type operators

    math.AP 2025-07 conditional novelty 7.0 of 10

    The limiting spectrum of high-contrast convolution-type operators is characterized via a beta function and generally contains extra contributions beyond the two-scale limit operator's spectrum.

  2. Quantitative estimates for high-contrast random media

    math.AP 2025-02 conditional novelty 6.0 of 10

    For elliptic equations with random well-separated holes, the paper proves stretched-exponential tails for the regularity radius and sublinear corrector growth under a multiscale spectral gap condition.

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