Shape optimization solutions via Monge-Kantorovich equation

被引：67

作者：

Bouchitte, G ^{[1
]}

Buttazzo, G ^{[1
]}

Seppecher, P ^{[1
]}

机构：

[1] UNIV PISA,DIPARTIMENTO MATEMAT,I-56127 PISA,ITALY

来源：

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1997年 / 324卷 / 10期

关键词：

D O I：

10.1016/S0764-4442(97)87909-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the optimization problem max{epsilon(mu) : mu nonnegative measure, integral d mu = m}, where epsilon(mu) is the energy associated to mu: epsilon(mu) = inf{1/2 integral \du\(2) d mu - [f, u] : u is an element of D(R-n)}. The datum f is a signed measure with finite total variation and zero average. We show that the optimization problem above admits a solution which is not in L-1(R-n) in general. This solution comes out by solving a suitable Monge-Kantorovich equation.

引用

页码：1185 / 1191

页数：7

共 9 条

[1]

ALLAIRE G, 1993, EUR J MECH A-SOLID, V12, P839

[2]

Bendsoe M.P., 1989, STRUCTURAL OPTIMIZAT, V1, P193, DOI [10.1007/BF01650949, DOI 10.1007/BF01650949]

[3] Energies with respect to a measure and applications to low dimensional structures [J].