Accepted Paper

Inserted: 7 mar 2012
Last Updated: 18 jul 2013

Journal: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Year: 2013

Abstract:

We give a general monotonicity formula for local minimizers of free discontinuity problems which have a {\it critical} deviation from minimality, of order $d-1$. This result allows to prove partial regularity results (i.e. closedness and density estimates for the jump set) for a large class of free discontinuity problems involving general energies associated to the jump set, as for example free boundary problems with Robin conditions. In particular, we give a short proof to the De Giorgi-Carriero-Leaci result for the Mumford-Shah functional.

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