Volume 26, 2020
|Number of page(s)||20|
|Published online||10 February 2020|
Higher integrability for the gradient of Mumford-Shah almost-minimizers
Fachbereich Mathematik, Universität Hamburg,
* Corresponding author: firstname.lastname@example.org
Accepted: 11 October 2019
We extend a recent higher-integrability result for the gradient of minimizers of the Mumford-Shah functional to a suitable class of almost-minimizers. The extension crucially depends on an L∞ gradient estimate up to regular portions of the discontinuity set of an almost-minimizer.
Mathematics Subject Classification: 49N60 49Q20 / 26B30 / 94A08
Key words: Mumford-Shah energy / regularity theory / SBV functions / discontinuity set / almost-minimizers / higher integrability / excess decay
© EDP Sciences, SMAI 2020
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