Local Hölder regularity of minimizers for nonlocal variational problems

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 Hölder regularity as the original image. More precisely, if the datum is (locally) [Formula: see text]-Hölder continuous for some [Formula: see text], where [Formula: see text] is a parameter related to the nonlocal operator, we prove that the solution is also [Formula: see text]-Hölder continuous.