Boundary Homogenization of a Class of Obstacle Problems

摘要

We study the homogenization of a boundary obstacle problem on a C^(1,α)-domain D for some elliptic equations with uniformly elliptic coefficient matricesγ.For anyε∈R+,■D=Γ∪E,Γ∩∑=Фand Sε■∑with suitable assumptions,we prove that asεtends to zero,the energy minimizer u^(ε) of∫_(D)|γ▽u|^(2) dx,subject to u≥φcp on S_(ε),up to a subsequence,converges weakly in H^(1)(D)to u,which minimizes the energy functional∫D|r▽u|^(2)+∫∑(u-φ)^(2)-μ(x)dS_(x),whereμ(x)depends on the structure of Sεandφis any given function in C∞(D).