Some Remarks on Uniqueness and Regularity of Cheeger Sets
Vicent Caselles, Antonin Chambolle, Matteo Novaga · Rendiconti del Seminario Matematico della Università di Padova · 2010
We show that generically the subsets of \mathbb R^N 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} .