由Hrmander向量场构成的抛物方程的W_*^(1,p)正则性  

W_*^(1,p)Regularity for Parabolic Equations Structured on Hrmander's Vector Fields

作　　者：朱茂春[1] 

机构地区：[1]北京师范大学数学科学学院,北京100875

出　　处：《数学年刊（A辑）》2014年第1期1-20,共20页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11001221,No.11271299)的资助

摘　　要：设X_1,…,X_q(q<n)是有界区域ΩR^n上的一组光滑Hrmander向量场.考虑下面的散度型抛物方程:u_t+X_i~*(a_(ij)(x,t)X_ju)=X_i~*f_i,其中X_i~*是X_i的形式伴随,系数a_(ij)(x,t)(i,j=1,2,…,q)是定义在Ω_T=Ω×(0,T)∈R^(n+1)上满足一致椭圆性条件的有界可测函数.在系数属于VMO_(loc)∩L~∞函数空间的情况下,得到了抛物方程弱解的内W_*^(1,p)正则性.Let W1,p＊ be a family of real smooth vector fields satisfying HSrmander＇s condition in a bounded domain Ω Rn. We are concerned with the following divergence parabolic equation： ut＋x＊i（aij（x,）Xju）=X＊i fi where X＊i is the formal adjoint of Xi, the coefficients aij（x,t） （i,j = 1,2,… ,q）valued bounded measurable functions defined in ΩT=Ω×（0,T）∈Rn＋1 , satisfying the uniform ellipticity condition. Under the assumption that the coefficients aij（x, t） belong to the space VMOloc∩L∞, the interior WI＇p regularity for weak solutions of the equation above is established.

关 键 词：散度型抛物方程 W1 p＊ 正则性 Hormander向量场 弱紧性 不连续系数 

分 类 号：O175.26[理学—数学]