Homogenization of elliptic equations with large random potential

2013/11/23 by Guillaume Bal, Bal, Guillaume, Ningyao Zhang +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1311.6040

openalex publication_date 2013/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an elliptic equation with purely imaginary, highly heterogeneous, and large random potential with a sufficiently rapidly decaying correlation function. We show that its solution is well approximated by the solution to a homogeneous equation with a real-valued homogenized potential as the correlation length of the random medium ε→ 0 and estimate the size of the random fluctuations in the setting d≥3.

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