Calculus of Variations and Geometric Measure Theory
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M. Focardi

Fine regularity results for Mumford-Shah minimizers: porosity, higher integrability and the Mumford-Shah conjecture

created by focardi on 12 Oct 2016
modified on 31 Oct 2016


CRM series 19

Inserted: 12 oct 2016
Last Updated: 31 oct 2016

Year: 2016

We review some classical results and more recent insights about the regularity theory for local minimizers of the Mumford and Shah energy and their connections with the Mumford and Shah conjecture. We discuss in details the links among the latter, the porosity of the jump set and the higher integrability of the approximate gradient. In particular, higher integrability turns out to be related with an explicit estimate on the Hausdorff dimension of the singular set and an energetic characterization of the conjecture itself.


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