@Article{AAM-38-2,
author = {Li, Jingzhi and Liu, Hongyu and Tang, Lan and Wang, Jiangwen},
title = {Boundary Homogenization of a Class of Obstacle Problems},
journal = {Annals of Applied Mathematics},
year = {2022},
volume = {38},
number = {2},
pages = {240--260},
abstract = {<p style="text-align: justify;">We study the homogenization of a boundary obstacle problem on
a $C^{1,α}$-domain $D$ for some elliptic equations with uniformly elliptic coefficient
matrices $\gamma.$ For any $\epsilon \in \mathbb{R}_+,$ $∂D=\Gamma ∪Σ,$ $\Gamma ∩Σ=∅$ and $S_{\epsilon}\subset Σ$ with suitable assumptions, we prove that as $\epsilon$ tends to zero, the energy minimizer $u^{\epsilon}$ of $\int_D
|\gamma ∇u|^2dx,$ subject to $u≥\varphi$ on $S_{\epsilon},$ up to a subsequence, converges weakly in $H^1
(D)$ to $\tilde{u},$ which minimizes the energy functional $$\int_D
|\gamma∇u|^2+ \int_Σ
(u−\varphi)^2\_\mu (x)dS_x,$$ where $\mu (x)$ depends on the structure of $S_{\epsilon}$ and $\varphi$ is any given function in $C^∞(\overline{D}).$</p>},
issn = {},
doi = {https://doi.org/10.4208/aam.OA-2022-0001},
url = {https://global-sci.com/article/72633/boundary-homogenization-of-a-class-of-obstacle-problems}
}