Abstract
We study the convex lift of Mumford-Shah type functionals in the space of rectifiable currents and we prove a convex decomposition 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.
| Original language | English |
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| Journal | Journal of Convex Analysis |
| Volume | 25 |
| Issue number | 4 |
| Publication status | Published - 2018 |
| Externally published | Yes |