LOWER SEMICONTINUITY OF A CLASS OF FUNCTIONALSIN SBV_H  

作　　者：SongYingqing YangXiaoping LongFei 

机构地区：[1]Dept.ofMath.＆Calc.,HunanCityUniv.,Yiyang413000,China. [2]SchoolofScience,NanjingUniv.ofSci.＆Tech.,Nanjing210094,China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2005年第1期27-34,共8页高校应用数学学报（英文版）（B辑）

摘　　要：In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with dimension 2n+1,ΩHn is an open set and Δ~ _Hu denotes the approximate derivative of the absolute continuous part Da_Hu with respect to D_Hu.In addition,a Lusin type approximation theorem for a SBV_H function is proved.In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with dimension 2n+1,ΩHn is an open set and Δ~ _Hu denotes the approximate derivative of the absolute continuous part Da_Hu with respect to D_Hu.In addition,a Lusin type approximation theorem for a SBV_H function is proved.

关 键 词：lower semicontinuity SBV_H function Heisenberg group Lusin approximation. 

分 类 号：O177[理学—数学]