Interior Hlder and gradient estimates for the homogenization of the linear elliptic equations  

作　　者：ZHANG QiaoFu CUI JunZhi 

机构地区：[1]LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Science China Mathematics》2013年第8期1575-1584,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.90916027);Special Funds for National Basic Research Program of China (973 Program) (Grant No. 2010CB832702);the State Key Laboratory of Scientific and Engineering Computing

摘　　要：H61der and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius＇s gradient estimate. If the coefficients are piecewise smooth and the homogenized solution is smooth enough, the interior error of the first-order expansion is O（e） in the HSlder norm; it is O（e） in W1,∞ based on the Avellaneda-Lin＇s gradient estimate when the coefficients are Lipschitz continuous. These estimates can be partly extended to the nonlinear parabolic equations.Hlder and gradient estimates for the correctors in the homogenization are presented based on the translation invariance and Li-Vogelius's gradient estimate.If the coefficients are piecewise smooth and the homogenized solution is smooth enough,the interior error of the first-order expansion is O(ε) in the Hlder norm;it is O(ε) in W 1,∞ based on the Avellaneda-Lin's gradient estimate when the coefficients are Lipschitz continuous.These estimates can be partly extended to the nonlinear parabolic equations.

关 键 词：gradient estimate HOMOGENIZATION translation invariance de Giorgi-Nash estimate 

分 类 号：O175.25[理学—数学] TP391.41[理学—基础数学]