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 g...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.展开更多
Let LSC(X) denote the set of all proper lower semicontinuous functions on X with the epi-topology. In this paper we give characterizations of the separation axioms. Baire properties and metrizability of LSC(X). We sho...Let LSC(X) denote the set of all proper lower semicontinuous functions on X with the epi-topology. In this paper we give characterizations of the separation axioms. Baire properties and metrizability of LSC(X). We show also that the continuous function space C(X) with the epi-topology is of first category when N is first countable.展开更多
文摘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.
文摘Let LSC(X) denote the set of all proper lower semicontinuous functions on X with the epi-topology. In this paper we give characterizations of the separation axioms. Baire properties and metrizability of LSC(X). We show also that the continuous function space C(X) with the epi-topology is of first category when N is first countable.
