Persistence of Hölder continuity for non-local integro-differential equations

2011/12/28 by Kyudong Choi, Choi, Kyudong
Mathematics · #35B45 #45G05 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B45 #msc:45G05 #msc:47G20

paper · pdf · doi:10.48550/arxiv.1112.6064

28 pages

arxiv created 2011/12/28 · arxiv updated 2011/12/30

Abstract

In this paper, we consider non-local integro-differential equations under certain natural assumptions on the kernel, and obtain persistence of Hölder continuity for their solutions. In other words, we prove that a solution stays in C^β for all time if its initial data lies in C^β. This result has an application for a fully non-linear problem, which is used in the field of image processing. The proof is in the spirit of the paper [18] of Kiselev and Nazarov where they established Hölder continuity of the critical surface quasi-geostrophic (SQG) equation.

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