Shape optimization problems on metric measure spaces

被引：7

作者：

Buttazzo, Giuseppe ^{[1
]}

Velichkov, Bozhidar ^{[2
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

[2] Scuola Normale Super Pisa, I-56126 Pisa, Italy

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 264卷 / 01期

关键词：

Shape optimization; Metric spaces; Capacity; Eigenvalues; Sobolev spaces; DIRICHLET PROBLEMS; VECTOR-FIELDS;

D O I：

10.1016/j.jfa.2012.09.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider shape optimization problems of the form min{J(Omega): Omega subset of X, m(Omega) <= c}, where X is a metric measure space and J is a suitable shape functional. We adapt the notions of gamma-convergence and weak-gamma convergence to this new general abstract setting to prove the existence of an optimal domain. Several examples are pointed out and discussed. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：1 / 33

页数：33

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