TY - JOUR
AU - Choi, Kyudong
DA - 2013/05
UR - https://scholarworks.unist.ac.kr/handle/201301/13063
AB - In this paper, we consider non-local integro-differential equations under certain natural assumptions on the kernel, and obtain persistence of Holder continuity for their solutions. In other words, we prove that a solution stays in C-beta for all time if its initial data lies in C-beta. This result has an application for a fully non-linear problem, which is used in the field of image processing. In addition, we show Holder regularity for solutions of drift diffusion equations with supercritical fractional diffusion under the assumption b is an element of (LC1-alpha)-C-infinity on the divergent-free drift velocity. The proof is in the spirit of [23] where Kiselev and Nazarov established Holder continuity of the critical surface quasi-geostrophic (SQG) equation.
LA - 영어
PB - AMER INST MATHEMATICAL SCIENCES
TI - Persistence of Holder continuity for non-local integro-differential equations
DO - 10.3934/dcds.2013.33.1741
ER -