Published Paper
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Inserted: 22 jul 2020
Last Updated: 9 nov 2026

Journal: Journal of Convex Analysis
Volume: 28
Year: 2021

Abstract:

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

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