Calculus of Variations and Geometric Measure Theory

G. Buttazzo - F. P. Maiale

Shape optimization problems for functionals with a boundary integral

created by buttazzo on 22 Jul 2020


Accepted Paper

Inserted: 22 jul 2020
Last Updated: 22 jul 2020

Year: 2020


We consider shape optimization problems for general integral functionals of the calculus of variations that may contain a boundary term. In particular, this class includes optimization problems governed by elliptic equations with a Robin condition on the free boundary. We show the existence of an optimal domain under rather general assumptions and we study the cases when the optimal domains are open sets and have a finite perimeter.

Keywords: shape optimization, integral functionals, finite perimeter, Robin condition