We give a more elementary proof of a result by Ambrosio, Fusco and Hutchin- son to estimate the Hausdorff dimension of the singular set of minimizers of the Mumford– Shah energy (see [1, Theorem 5.6]). On the one hand, we follow the strategy of the above mentioned paper; but on the other hand our analysis greatly simplifies the argument since it relies on the compactness result proved by the first two authors in [4, Theorem 13] for sequences of local minimizers with vanishing gradient energy, and the regularity theory of minimal Caccioppoli partitions, rather than on the corresponding results for Almgren’s area minimizing sets.
De Lellis C, Focardi M, Ruffini B (2014). A note on the Hausdorff dimension of the singular set for minimizers of the Mumford-Shah energy. ADVANCES IN CALCULUS OF VARIATIONS, 7, 539-545 [10.1515/acv-2013-0107].
A note on the Hausdorff dimension of the singular set for minimizers of the Mumford-Shah energy
Ruffini B
2014
Abstract
We give a more elementary proof of a result by Ambrosio, Fusco and Hutchin- son to estimate the Hausdorff dimension of the singular set of minimizers of the Mumford– Shah energy (see [1, Theorem 5.6]). On the one hand, we follow the strategy of the above mentioned paper; but on the other hand our analysis greatly simplifies the argument since it relies on the compactness result proved by the first two authors in [4, Theorem 13] for sequences of local minimizers with vanishing gradient energy, and the regularity theory of minimal Caccioppoli partitions, rather than on the corresponding results for Almgren’s area minimizing sets.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
