Published Paper
Inserted: 21 jun 2019
Last Updated: 9 dec 2023
Journal: Adv. Calc. Var.
Volume: 15
Number: 2
Pages: 213-234
Year: 2022
Doi: 10.1515/acv-2019-0050
Abstract:
We introduce a notion of connected perimeter for planar sets defined as the lower semicontinuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is also studied.
We prove a representation formula which links the connected perimeter, the classical perimeter, and the length of suitable Steiner trees. We also discuss the application of this notion to the existence of solutions to a nonlocal minimization problem.
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