ON CONVERGENCE OF BOUNDARY HAUSDORFF MEASURE AND APPLICATION TO A BOUNDARY SHAPE OPTIMIZATION PROBLEM

被引：10
|
作者：
Guo, Bao-Zhu [1 ,2 ,3 ]
Yang, Dong-Hui [2 ,4 ]
机构：
[1] Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China
[2] Univ Witwatersrand, Sch Computat & Appl Math, Johannesburg, South Africa
[3] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Peoples R China
[4] Cent S Univ Changsha, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2013年 / 51卷 / 01期
基金：
新加坡国家研究基金会; 中国国家自然科学基金;
关键词：
shape optimization; Hausdorff measure; existence of shape optimal solution;
D O I：
10.1137/110853765
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This is the second part of our recent work [SIAM J. Control Optim., 50 (2012), pp. 222-242] on new open sets class and related shape optimization. In this paper, we are concerned with a boundary shape optimization problem. It is shown that the convergence of the open sets class under the Hausdorff distance implies the convergence of the Hausdorff measure on the boundary. The existence of the boundary shape optimization is concluded.
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页码：253 / 272
页数：20
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