EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP H^n

• Published in: Acta mathematica scientia Vol. 25; no. 3; pp. 455 - 469
• Main Author: 宋迎清 杨孝平 秦姣华
• Format: Journal Article
• Language: English
• Published: 01.07.2005
• Subjects: 存在性; 数学物理; 海森伯格群; 能量导数; 自由连续
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(05)60009-4

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).