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
In this paper we aim to show a compactness theorem for SBVH(Ω) of special functions u with bounded variation and with ↓△H^c u=0 in the Heisenberg group H^n.
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In this paper we aim to show a compactness theorem for SBVH(Ω) of special functions u with bounded variation and with ↓△H^c u=0 in the Heisenberg group H^n.
