EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP H^n - 宋迎清 杨孝平 秦姣华 (Acta mathematica scientia, 2005)
The purpose of this paper is to prove existence of minimisers of the functional J(K, u) :=∫Ω/kf(Lu)dx+α∫Ω/k|u-g|^qdx+βSd^Q-1(K∩Ω),where Ω is an open set of the Heisenberg group H^n, K runs over all closed sets of H^n, u varies in CH^1(Ω\K), α, β >0, q ≥1, g∈ L^q(Ω) ∩L^∞(Ω) and f : R^2n →R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below).