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

created by buttazzo on 11 Jul 2020

[BibTeX]

Accepted Paper

Inserted: 11 jul 2020
Last Updated: 11 jul 2020

Year: 2020

Abstract:

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.