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Posted online: 2018-06-15 11:18:06Z by Giuseppe Buttazzo
Cite as: P-180615.1
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We consider shape optimization problems for general integral functionals of the calculus of variations, defined on a domain Ω that varies over all subdomains of a given bounded domain D of Rd. 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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