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 Holder regularity as the original image. More precisely, if the datum is (locally) β-Holder continuous for some β (1-s, 1], where s (0, 1) is a parameter related to the nonlocal operator, we prove that the solution is also β-Holder continuous.
Local Hölder regularity of minimizers for nonlocal variational problems
Novaga, Matteo;
2023-01-01
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 Holder regularity as the original image. More precisely, if the datum is (locally) β-Holder continuous for some β (1-s, 1], where s (0, 1) is a parameter related to the nonlocal operator, we prove that the solution is also β-Holder continuous.File in questo prodotto:
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