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 ${f R}^d$. 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.
Optimal shapes for general integral functionals
Giuseppe Buttazzo
;Harish Shrivastava
2020-01-01
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 ${f R}^d$. 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.File in questo prodotto:
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