Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 931-934

A SHORT PROOF OF HÖLDER CONTINUITY FOR FUNCTIONS IN DEGIORGI CLASSES

Colin Klaus and Naian Liao

Ohio State University, The Mathematical Biosciences Institute
Columbus, OH 43210, U.S.A.; klaus.68 'at' mbi.osu.edu

Chongqing University, College of Mathematics and Statistics
Chongqing, 401331, P.R. China; liaon 'at' cqu.edu.cn

Abstract. The goal of this note is to give an alternative proof of local Hölder continuity for functions in DeGiorgi classes based on an idea of Moser.

2010 Mathematics Subject Classification: Primary 35B65; Secondary 35J62, 35J92, 49N60.

Key words: DeGiorgi classes, Hölder continuity, Moser's method.

Reference to this article: C. Klaus and N. Liao: A short proof of Hölder continuity for functions in DeGiorgi classes. Ann. Acad. Sci. Fenn. Math. 43 (2018), 931-934.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4354