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arXiv · 2410.09378

Homogenization of an obstacle problem with highly oscillating coefficients and obstacles

Sunghoon Kim·Ki-Ahm Lee·Se-Chan Lee·Minha Yoo
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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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Sunghoon Kim, Ki-Ahm Lee, Se-Chan Lee, Minha Yoo. 2024-10-12. Homogenization of an obstacle problem with highly oscillating coefficients and obstacles. https://arxiv.org/abs/2410.09378

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