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arXiv · 2007.05725

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

Giuseppe Buttazzo·Francesco Paolo Maiale
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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.

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Giuseppe Buttazzo, Francesco Paolo Maiale. 2020-07-11. Optimal one-dimensional structures for the principal eigenvalue of two-dimensional domains. https://arxiv.org/abs/2007.05725

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