A discrete coarea-type formula for the Mumford-Shah functional in dimension one

  • Marcello Carioni (Universität Leipzig)
G3 10 (Lecture hall)


We consider 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. Then 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 space dimension.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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