Rendiconti del Seminario Matematico della Università di Padova


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Volume 123, 2010, pp. 191–201
DOI: 10.4171/RSMUP/123-9

Published online: 2010-06-30

Some Remarks on Uniqueness and Regularity of Cheeger Sets

Vicent Caselles, Antonin Chambolle[1] and Matteo Novaga[2]

(1) Ecole Polytechnique, Palaiseau, France
(2) Università di Pisa, Italy

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 C1,1, when the ambient set is C1,1.

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Caselles Vicent, Chambolle Antonin, Novaga Matteo: Some Remarks on Uniqueness and Regularity of Cheeger Sets. Rend. Sem. Mat. Univ. Padova 123 (2010), 191-201. doi: 10.4171/RSMUP/123-9