Symmetry breaking for a problem in optimal insulation

被引：26

作者：

Bucur, Dorin ^{[1
]}

Buttazzo, Giuseppe ^{[2
]}

Nitsch, Carlo ^{[3
]}

机构：

[1] Univ Savoie Mt Blanc, Lab Math LAMA, Inst Univ France, Campus Sci, F-73376 Le Bourget Du Lac, France

[2] Univ Pisa, Dipartimento Matemat, Largo B Pontecorvo 5, I-56127 Pisa, Italy

[3] Univ Naples Federico II, Dipartimento Matemat & Applicaz, Via Cintia, I-80126 Naples, Italy

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2017年 / 107卷 / 04期

关键词：

Optimal insulation; Symmetry breaking; Robin boundary conditions; REINFORCEMENT;

D O I：

10.1016/j.matpur.2016.07.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem of optimally insulating a given domain Omega of R-d; this amounts to solve a nonlinear variational problem, where the optimal thickness of the insulator is obtained as the boundary trace of the solution. We deal with two different criteria of optimization: the first one consists in the minimization of the total energy of the system, while the second one involves the first eigenvalue of the related differential operator. Surprisingly, the second optimization problem presents a symmetry breaking in the sense that for a ball the optimal thickness is nonsymmetric when the total amount of insulator is small enough. In the last section we discuss the shape optimization problem in which 12 is allowed to vary too. (C) 2016 Elsevier Masson SAS. All rights reserved.

引用

页码：451 / 463

页数：13

共 12 条

[1] REINFORCEMENT PROBLEMS IN THE CALCULUS OF VARIATIONS [J].