Optimal one-dimensional structures for the principal eigenvalue of two-dimensional domains

被引：1
|
作者：
Buttazzo, Giuseppe [1 ]
Maiale, Francesco Paolo [2 ]
机构：
[1] Univ Pisa, Dipartimento Matemat, Largo B Pontecorvo 5, I-56127 Pisa, Italy
[2] Scuola Normale Super Pisa, Piazza Cavalieri 7, I-56126 Pisa, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 191卷
关键词：
Optimal reinforcement; Eigenvalues of the Laplacian; Stiffeners; Fastest cooling; REGULARITY; NETWORKS;
D O I：
10.1016/j.na.2019.111627
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A shape optimization problem arising from the optimal reinforcement of a membrane by means of one-dimensional stiffeners or from the fastest cooling of a two-dimensional object by means of "conducting wires" is considered. The criterion we consider is the maximization of the first eigenvalue and the admissible classes of choices are the one of one-dimensional sets with prescribed total length, or the one where the constraint of being connected (or with an a priori bounded number of connected components) is added. The corresponding relaxed problems and the related existence results are described. (C) 2019 Elsevier Ltd. All rights reserved.
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页数：26
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