Title | A note on the Hausdorff dimension of the singular set for minimizers of the Mumford-Shah functional |
Publication Type | Journal Article |
Year of Publication | 2014 |
Authors | De Lellis C., Focardi M., Ruffini B. |
Journal | Advances in Calculus of Variations |
Volume | 7 |
Pagination | 539–545 |
Publisher | De Gruyter |
Type of Article | geometric measure theory |
ISSN | 1864-8258 |
Abstract | 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. |
Notes | Adv. Calc. Var. 7, pp. 539-545, 2014 |
URL | https://www.degruyter.com/view/j/acv.2014.7.issue-4/acv-2013-0107/acv-2013-0107.xml?format=INT |
DOI | 10.1515/acv-2013-0107 |
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