Homogenization of an obstacle problem with highly oscillating coefficients and obstacles

2024/10/12 by Sung‐Hoon Kim, Kim, Sunghoon, Ki-Ahm Lee +5
Computer Science · Engineering · Mathematics · #35B27 #35D40 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2410.09378

openalex publication_date 2024/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the viscosity method for the homogenization of an obstacle problem with highly oscillating obstacles. The associated operator, in non-divergence form, is linear and elliptic with variable coefficients. We first construct a highly oscillating corrector, which captures the singular behavior of solutions near periodically distributed holes of critical size. We then prove the uniqueness of a critical value that encodes the coupled effects of oscillations in both the coefficients and the obstacles.

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