Regularity of Minimizers of Shape Optimization Problems involving Perimeter

Guido De Philippis, Jimmy Lamboley, Michel Pierre +1

We prove existence and regularity of optimal shapes for the problem$$\min \{P(\Omega )+\mathcal{G}(\Omega ):\Omega \subset D,|\Omega |=m\},$$where $P$ denotes the perimeter, $|\cdot |$ is the vo…