EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP Hn

EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG

GROUP Hn

Song Yingqing;Yang Xiaoping;Qin Jiaohua

【期刊名称】《数学物理学报（英文版）》 【年(卷),期】2005(025)003

【摘要】The purpose of this paper is to prove existence of minimisers of the

functional

J(K,u):=∫ΩK

f(Lu)dx+α∫ΩK

|u

-

g|qdx+βSQ-

1d(K∩Ω),where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C1H(ΩK), α,β＞0,q ≥ 1,g ∈ Lq(Ω) ∩L∞(Ω) and f: R2n → R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below). 【总页数】15页(455-469) 【

关

键

词

】

SBVH

function;Heisenberg

group;minimiser;energy;deviation;free discontinuity problem 【作者】Song Yingqing;Yang Xiaoping;Qin Jiaohua

【作者单位】Department of Mathematics & Calculation, Hunan City University, Yiyang 413000, China;School of Science, Nanjing University of Science & Technology, Nanjing 210094, China;Department of Mathematics & Calculation, Hunan City University, Yiyang 413000, China 【正文语种】中文 【中图分类】O41