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arXiv · 1610.01846

A Convex Decomposition Formula for the Mumford-Shah Functional in Dimension One

Marcello Carioni
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Abstract

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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Marcello Carioni. 2016-10-06. A Convex Decomposition Formula for the Mumford-Shah Functional in Dimension One. https://arxiv.org/abs/1610.01846

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