Rendiconti del Seminario Matematico della Università di Padova

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

Some Remarks on Uniqueness and Regularity of Cheeger Sets

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

(1) CMAP, Ecole Polytechnique, CNRS, 91128, Palaiseau, France
(2) Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, 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