High-order Regularity Theory for High-contrast Elliptic Homogenization

2025/10/01 by Heikki Lohi, Lohi, Heikki
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2510.00737

39 pages

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

The purpose of this article is to formulate and prove a global high-order regularity result within the high-contrast framework of elliptic homogenization. In order to achieve this, we also present a version of the high-contrast Caccioppoli inequality.

Citations

• Renormalization group and elliptic homogenization in high contrast
• Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift
• Elliptic homogenization from qualitative to quantitative
• Quantitative stochastic homogenization of convex integral functionals

Related

• Renormalization group and elliptic homogenization in high contrast
• Large-Scale Lipschitz Estimates for Elliptic Systems with Periodic High-Contrast Coefficients
• A coarse-graining theory for elliptic operators and homogenization in high contrast
• Quantitative estimates for high-contrast random media
• Uniform Regularity Estimates in Homogenization Theory of Elliptic Systems with Lower Order Terms on the Neumann Boundary Problem