## 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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### References:

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