Calculus of Variations and Geometric Measure Theory
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S. Piontek - T. Schmidt

Higher integrability for the gradient of Mumford-Shah almost-minimizers

created by schmidt on 10 Oct 2019
modified on 18 Feb 2020


Published Paper

Inserted: 10 oct 2019
Last Updated: 18 feb 2020

Journal: ESAIM, Control Optim. Calc. Var.
Volume: 20
Year: 2020
Links: Link to the published version


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 $\mathrm{L}^\infty$ gradient estimate up to regular portions of the discontinuity set of an almost-minimizer.


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