Error estimate of the homogenization solution for elliptic problems with small periodic coefficients on L~∞(Ω)  

作　　者：HE WenMing1,2 & CUI JunZhi3 1Department of Mathematics,Wenzhou University,Wenzhou 325035,China 2School of Aeronautics and Astronautics,Zhejiang University,Hangzhou 310027,China 3LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China 

出　　处：《Science China Mathematics》2010年第5期194-215,共22页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.60971121,10590353,90916027,10725210);Major State Basic Research Development Program of China (973Program) (Grant No.2010CB832702);the State Key Laboratory of Science and Engineering Computing,Natural Science Foundation of Zhejiang Province,China (Grant No.Y6090108);Postdoctoral Science Foundation of China (Grant No.20090451454)

摘　　要：In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).

关 键 词：MULTI-SCALE HOMOGENIZATION theory HOMOGENIZATION SOLUTION second order ELLIPTIC equations with SMALL periodic coeficients 

分 类 号：O175.25[理学—数学]