[C21] Interdisciplinary Studies & Other disciplines

[C21-03] Homogenization of non-divergence type equation with oscillating coefficients defined on a highly oscillating obstacles.

*Minha Yoo¹, Sunghoon Kim², Ki-Ahm Lee³, Se-chan Lee⁴ (1. National Institute for Mathematical Sciences (Korea), 2. The Catholic University of Korea (Korea), 3. Seoul National University (Korea), 4. Korea Institute for Advanced Study (Korea))

Keywords:

homogenization,obstacle problem,elliptic partial differential equations

In this talk, we discuss the homogenization of a highly oscillating obstacle problem using the viscosity method. The equation we deal with is a non-divergence type equation with oscillating coefficients. To analyze the behavior of solutions in the obstacle problem, we construct a corrector function, periodic function when the obstacle is given as 1. By utilizing this corrector, we identify the so-called "strange term behavior" when the size of the domain where the obstacle is defined reaches a critical value. We then modify the corrector for critical size and analyze the solution's behavior when the size of the obstacle is either larger or smaller than the critical value.