# Local Hölder regularity of minimizers for nonlocal denoising problems

created by onoue on 16 Jul 2021
modified by novaga on 17 Jul 2021

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Submitted Paper

Inserted: 16 jul 2021
Last Updated: 17 jul 2021

Pages: 25
Year: 2021

Abstract:

We study the regularity of solutions to a nonlocal version of the image denoising model and we show that, in two dimensions, minimizers have the same Holder regularity as the original image. More precisely, if the datum is (locally) $\beta$-Hölder continuous for some $\beta\in(1-s,\,1]$, where $s\in (0,1)$ is a parameter related to the nonlocal operator, we prove that the solution is also $\beta$-Hölder continuous.