数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (3): 455-469.

• 论文 • 上一篇    下一篇

EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP Hn 1

宋迎清,杨孝平,秦姣华   

  1. Department of Mathematics &|Calculation, Hunan City University, Yiyang 413000, China
    2School of Science, Nanjing University of Science &|Technology, Nanjing 210094, China
  • 出版日期:2005-07-20 发布日期:2005-07-20
  • 基金资助:

    This work is supported by NNSF(10471063), Hunan NSF(03JJY4002) &
    Hunan Education Administration Item(03A011)

EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP Hn 1

 SONG Ying-Qing, YANG Xiao-Beng, QIN Jiao-Hua   

  • Online:2005-07-20 Published:2005-07-20
  • Supported by:

    This work is supported by NNSF(10471063), Hunan NSF(03JJY4002) &
    Hunan Education Administration Item(03A011)

PDF (PC)

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摘要：

The purpose of this paper is to prove existence of minimisers of
the functional
$$
J(K,u):=\int_{\Omega\setminus K}f(L_u){\rm d}x+\alpha
 \int_{\Omega\setminus K}|u-g|^q {\rm d}x+\beta \sdqe(K\cap\Omega),
$$
where $\Omega$ is an open set of the Heisenberg group
$\hn$, $K$ runs over all closed sets of $\hn$, $u$ varies in
$C_H^1(\Omega\setminus K)$, $\alpha$, $\beta >0,q\ge 1,g\in
 L^q(\Omega)\cap L^\infty(\Omega)$ and $f:R^{2n}
\rightarrow R$ is a
convex function  satisfying some
 structure conditions (H$_1$)(H$_2)$(H$_3)$ (see below).

Abstract:

The purpose of this paper is to prove existence of minimisers of
the functional
$$
J(K,u):=\int_{\Omega\setminus K}f(L_u){\rm d}x+\alpha
 \int_{\Omega\setminus K}|u-g|^q {\rm d}x+\beta \sdqe(K\cap\Omega),
$$
where $\Omega$ is an open set of the Heisenberg group
$\hn$, $K$ runs over all closed sets of $\hn$, $u$ varies in
$C_H^1(\Omega\setminus K)$, $\alpha$, $\beta >0,q\ge 1,g\in
 L^q(\Omega)\cap L^\infty(\Omega)$ and $f:R^{2n}
\rightarrow R$ is a
convex function  satisfying some
 structure conditions (H$_1$)(H$_2)$(H$_3)$ (see below).

Key words: SBVH function, Heisenberg group, minimiser;energy;deviation, free dis-
continuity problem

中图分类号: 

  • 26A45
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