| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 6 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/cocv/2019063 | |
| Published online | 10 February 2020 | |
Higher integrability for the gradient of Mumford-Shah almost-minimizers
Fachbereich Mathematik, Universität Hamburg,
Bundesstr. 55,
20146
Hamburg, Germany.
* Corresponding author: thomas.schmidt@math.uni-hamburg.de
Received:
28
March
2019
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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