Potential theoretic approach to Schauder estimates for the fractional Laplacian

Claudia Bucur, Aram Karakhanyan

Research output: Contribution to journalArticlepeer-review

Abstract

We present an elementary approach for the proof of Schauder estimates for the equation $ (-\Delta )^s u(x)=f(x), \,0<s<1$, with $ f$ having a modulus of continuity $ \omega _f$, based on the Poisson representation formula and dyadic ball approximation argument. We give the explicit modulus of continuity of $ u$ in balls $ B_r(x)\subset \mathbb{R}^n$ in terms of $ \omega _f$.
Original languageEnglish
Pages (from-to)637-651
Number of pages14
JournalProceedings of the american mathematical society
Volume145
Issue number2
Early online date26 Jul 2016
DOIs
Publication statusPublished - Feb 2017

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