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arXiv · 1602.05359

Potential theoretic approach to Schauder estimates for the fractional Laplacian

Claudia Bucur·Aram L. Karakhanyan
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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 $\omega_f$.

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Claudia Bucur, Aram L. Karakhanyan. 2016-02-17. Potential theoretic approach to Schauder estimates for the fractional Laplacian. https://doi.org/10.1090/proc/13227

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