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).
基金
partially supported by the NSF of China No.11971221
Guangdong NSF Major Fund No.2021ZDZX1001
the Shenzhen Sci-Tech Fund Nos.RCJC20200714114556020,JCYJ20200109115422828,JCYJ20190809150413261
Guangdong Provincial Key Laboratory of Computational Science and Material Design No.2019B030301001
supported by the startup fund from City University of Hong Kong and the Hong Kong RGC General Research Fund(projects Nos.12301420,12302919 and 12301218)
partially supported by NNSFC grants of China(No.11831009)
the Fundamental Research Funds for the Central Universities(No.CCNU19TS032)
partially supported by the Shenzhen Sci-Tech Fund No.JCYJ20180307151603959。
