# Local Hölder regularity of minimizers for nonlocal variational problems

created by onoue on 16 Jul 2021
modified on 27 Jul 2022

[BibTeX]

Accepted Paper

Inserted: 16 jul 2021
Last Updated: 27 jul 2022

Journal: Communications in Contemporary Mathematics
Pages: 27
Year: 2022

Abstract:

We study the regularity of solutions to a nonlocal variational problem, which is related to the image denoising model, and we show that, in two dimensions, minimizers have the same H\"older regularity as the original image. More precisely, if the datum is (locally) $\beta$-H\"older 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 $\beta$-H\"older continuous.