Calculus of Variations and Geometric Measure Theory

G. Buttazzo - H. Shrivastava

Optimal shapes for general integral functionals

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


Published Paper

Inserted: 25 mar 2018
Last Updated: 2 jun 2022

Journal: Annales Henry Lebesgue
Year: 2019

ArXiv: 1803.09310 PDF


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.

Keywords: shape optimization, integral functionals, quasi open sets, finite perimeter