# Regularity Results for an Optimal Design Problem \dots]{Regularity Results for an Optimal Design Problem with lower order terms

created by lamberti on 13 Nov 2021

[BibTeX]

Submitted Paper

Inserted: 13 nov 2021
Last Updated: 13 nov 2021

Year: 2021

Abstract:

We study the regularity of the interface for optimal energy configurations of functionals involving bulk energies with an additional perimeter penalization of the interface. It is allowed the dependence on $(x,u)$ for the bulk energy. For a minimal configuration $(E,u)$, the H\"{o}lder continuity of $u$ is well known. We give an estimate for the singular set of the boundary $\partial E$. Namely we show that the Hausdorff dimension of the singular set is strictly smaller than $n-1$.

Download:

Credits | Cookie policy | HTML 5 | CSS 2.1