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| Boundary Homogenization of a Class of Obstacle Problems |
| Jingzhi Li,Hongyu Liu,Lan Tang,Jiangwen Wang |
| (Department of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China;SUSTech International Center for Mathematics, Shenzhen,Guangdong 518055, China; National Center for Applied Mathematics, Shenzhen, Guangdong 518055,China;Department of Mathematics, City University of Hong Kong, Kowloon,Hong Kong, China;School of Mathematics and Statistics, Central China Normal University,Wuhan, Hubei 430079, China) |
| DOI： |
| Abstract: |
| 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 γ. For any ∈R+, ?D=Γ∪Σ, Γ∩Σ=? and S ?Σ with suitable assumptions, we prove that as tends to zero, the energy minimizer u
of R D
|γ?u|
2dx,
subject to u≥? on Sε, up to a subsequence, converges weakly in H1
(D) to ?u,
which minimizes the energy functional
Z
D
|γ?u|
2+
Z
Σ
(u??)
2
?μ(x)dSx,
where μ(x) depends on the structure of S and ? is any given function in C∞(D). |
| Key words: Homogenization, boundary obstacle, correctors, asymptotic analysis |