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A note on the Hausdorff dimension of the singular setfor minimizers of the Mumford-Shah energy

De Lellis, Camillo ; Focardi, Matteo ; Ruffini, Berardo

In: Advances in Calculus of Variations, 2014, vol. 7, no. 4, p. 539-545

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    Title
    • A note on the Hausdorff dimension of the singular setfor minimizers of the Mumford-Shah energy
    Author
    • De Lellis, Camillo. Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
    • Focardi, Matteo. Università di Firenze, DiMaI "U. Dini”, V. le Morgagni 67/A,I-50134 Firenze, Italy
    • Ruffini, Berardo. Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 4, I-56126 Pisa, Italy
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Advances in Calculus of Variations, 2014, vol. 7, no. 4, p. 539-545. De Gruyter
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:303799
    Summary
    We give a more elementary proof of a result by Ambrosio, 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), no. 2, 187-215, 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 [J. Math. Pures Appl. 100 (2013), 391-409, 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