Lower semicontinuity of A class of functionals in SBV H

Abstract

In this paper lower semicontinuity of the functional I(u)=∫ Ω f(x,u,Δ Hu)dx is investigated for f being a Caratheodory function defined on H n × R × R2n and for u∈SBV H (Ω), where H n is the Heisenberg group with dimension 2n+1, Ω∩H n is an open set and ∇ Hu denotes the approximate derivative of the absolute continuous part D a Hu with respect to D Hu. In addition, a Lusin type approximation theorem for a SBV H function is proved.