# 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 language English 637-651 14 Proceedings of the american mathematical society 145 2 26 Jul 2016 https://doi.org/10.1090/proc/13227 Published - Feb 2017