Calculus of Variations and Geometric Measure Theory
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M. Carioni

A convex decomposition formula for the Mumford-Shah functional in dimension one

created by carioni on 07 Mar 2017
modified on 13 Apr 2019


Published Paper

Inserted: 7 mar 2017
Last Updated: 13 apr 2019

Journal: Journal of Convex Analysis
Year: 2018


We study the convex lift of Mumford-Shah type functionals in the space of rectifiable currents and we prove a generalized coarea formula in dimension one, for finite linear combinations of SBV graphs. We use this result to prove the equivalence between the minimum problems for the Mumford-Shah functional and the lifted one and, as a consequence, we obtain a weak existence result for calibrations in one dimension.


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