Calculus of Variations and Geometric Measure Theory

G. Buttazzo - F. P. Maiale

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

created by buttazzo on 11 Jul 2020


Accepted Paper

Inserted: 11 jul 2020
Last Updated: 11 jul 2020

Year: 2020


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.

Keywords: stiffeners, Optimal reinforcement, eigenvalues of the Laplacian, fastest cooling