Optimal one-dimensional structures for the principal eigenvalue of two-dimensional domains
Analysis of PDEs
2020-07-14 v1 Optimization and Control
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.
Cite
@article{arxiv.2007.05725,
title = {Optimal one-dimensional structures for the principal eigenvalue of two-dimensional domains},
author = {Giuseppe Buttazzo and Francesco Paolo Maiale},
journal= {arXiv preprint arXiv:2007.05725},
year = {2020}
}
Comments
32 pages, 2 figures