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Choi, Kyudong
Fluids Analysis Lab
Research Interests
  • fluid equations, mathematical biology, conservation laws,

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

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Title
Persistence of Holder continuity for non-local integro-differential equations
Author
Choi, Kyudong
Issue Date
2013-05
Publisher
AMER INST MATHEMATICAL SCIENCES
Citation
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.33, no.5, pp.1741 - 1771
Abstract
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.
URI
https://scholarworks.unist.ac.kr/handle/201301/13063
URL
https://www.aimsciences.org/journals/displayArticles.jsp?paperID=8007
DOI
10.3934/dcds.2013.33.1741
ISSN
1078-0947
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MTH_Journal Papers
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