Persistence of H\"{o}lder continuity for non-local integro-differential equations

Kyudong Choi

Persistence of H\"{o}lder continuity for non-local integro-differential equations

Analysis of PDEs 2011-12-30 v1

Authors: Kyudong Choi

Abstract

In this paper, we consider non-local integro-differential equations under certain natural assumptions on the kernel, and obtain persistence of H\"{o}lder 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. The proof is in the spirit of the paper [18] of Kiselev and Nazarov where they established H\"{o}lder continuity of the critical surface quasi-geostrophic (SQG) equation.

Keywords

integro-differential equation holder continuity non-local operator persistence critical surface quasi-geostrophic equation image processing

Cite

@article{arxiv.1112.6064,
  title  = {Persistence of H\"{o}lder continuity for non-local integro-differential equations},
  author = {Kyudong Choi},
  journal= {arXiv preprint arXiv:1112.6064},
  year   = {2011}
}

Comments

28 pages

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