Work

High-contrast random systems of PDEs: Homogenization and spectral theory

Year: 2025

Type: article

Abstract: We develop a qualitative homogenization and spectral theory for elliptic systems of partial differential equations in divergence form with highly contrasting (i.e. non-uniformly elliptic) random coefficients. The focus of this paper is on the behavior of the spectrum as the heterogeneity parameter tends to zero; in particular, we show that in general one does not have Hausdorff convergence of spectra. The theoretical analysis is complemented by several explicit examples, showcasing the wider range of applications and physical effects of systems with random coefficients, when compared with systems with periodic coefficients or with scalar operators (both random and periodic).

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199725500294

Authors: Matteo Capoferri, Mikhail Cherdantsev, Igor Velčić