TY - UNPB
T1 - Quantitative estimates for high-contrast random media
AU - Bella, Peter
AU - Capoferri, Matteo
AU - Cherdantsev, Mikhail
AU - Velčić, Igor
N1 - 42 pages
PY - 2025/2/13
Y1 - 2025/2/13
N2 - 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 (https://arxiv.org/abs/2502.02847).
AB - 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 (https://arxiv.org/abs/2502.02847).
KW - math.AP
KW - math-ph
KW - math.MP
KW - math.PR
KW - 35J70, 60H25 (primary) 35B27, 35B40, 74A40, 74Q05 (secondary)
U2 - 10.48550/arXiv.2502.09493
DO - 10.48550/arXiv.2502.09493
M3 - Preprint
BT - Quantitative estimates for high-contrast random media
PB - arXiv
ER -