Optimal shapes for general integral functionals

created by buttazzo on 25 Mar 2018
modified by shrivastava1 on 02 Jun 2022

[BibTeX]

Published Paper

Inserted: 25 mar 2018
Last Updated: 2 jun 2022

Journal: Annales Henry Lebesgue
Year: 2019

ArXiv: 1803.09310 PDF

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.