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Some remarks on uniqueness and regularity of Cheeger sets. (English) Zbl 1198.49042

Summary: We show that generically the subsets of RN with finite volume have a unique Cheeger set, in the sense that there always exists a nearby set which has a unique Cheeger set. We also prove that Cheeger sets are \(C^{1,1}\), when the ambient set is \(C^{1,1}\).

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
49N60 Regularity of solutions in optimal control
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