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arXiv · 1803.09310

Optimal shapes for general integral functionals

Giuseppe Buttazzo·Harish Shrivastava
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Abstract

We consider shape optimization problems for general integral functionals of the calculus of variations, defined on a domain $\Omega$ that varies over all subdomains of a given bounded domain $D$ of ${\bf R}^d$. We show in a rather elementary way the existence of a solution that is in general a quasi open set. Under very mild conditions we show that the optimal domain is actually open and with finite perimeter. Some counterexamples show that in general this does not occur.

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Giuseppe Buttazzo, Harish Shrivastava. 2018-03-25. Optimal shapes for general integral functionals. https://arxiv.org/abs/1803.09310

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