We give a more elementary proof of a result by Ambrosio and Fusco and Hutchinson to estimate the Hausdorff dimension of the singular set of minimizers of the Mumford?Shah energy (see [Calc. Var. Partial Differential Equations 16 (2003) and no. 2 and 187?215 and Theorem 5.6]). On the one hand and 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 [J. Math. Pures Appl. 100 (2013) and 391?409 and Theorem 13] for sequences of local minimizers with vanishing gradient energy and and the regularity theory of minimal Caccioppoli partitions and rather than on the corresponding results for Almgren's area minimizing sets.

Adv. Calc. Var. 7, pp. 539-545, 2014