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.
Cite this article
Vicent Caselles, Antonin Chambolle, Matteo Novaga, Some Remarks on Uniqueness and Regularity of Cheeger Sets. Rend. Sem. Mat. Univ. Padova 123 (2010), pp. 191–201