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

Kyudong Choi
2012 Discrete and Continuous Dynamical Systems. Series A  
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. In addition, we show Hölder regularity for solutions of drift diffusion equations with supercritical
more » ... supercritical fractional diffusion under the assumption b ∈ L ∞ C 1−α on the divergent-free drift velocity. The proof is in the spirit of [23] where Kiselev and Nazarov established Hölder continuity of the critical surface quasi-geostrophic (SQG) equation. 2010 Mathematics Subject Classification. Primary: 35B45, 45G05, 47G20.
doi:10.3934/dcds.2013.33.1741 fatcat:rhzzgic75bcvph5yjwd33qeuia