Calculus of Variations and Geometric Measure Theory
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L. Esposito - L. Lamberti

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


Submitted Paper

Inserted: 13 nov 2021
Last Updated: 13 nov 2021

Year: 2021


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 $n-1$.

Keywords: free boundary, minimal surfaces, perimeter penalization, volume constraint


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