We present an elementary approach for the proof of Schauder estimates for the equation (−Δ)su(x) = f(x), 0 < s < 1, with f having a modulus of continuity ωf, based on the Poisson representation formula and dyadic ball approximation argument. We give the explicit modulus of continuity of u in balls Br(x) ⊂ Rn in terms of ωf.
Bucur, C., Karakhanyan, A. (2017). Potential theoretic approach to Schauder estimates for the fractional Laplacian. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145(2), 637-651 [10.1090/proc/13227].
Potential theoretic approach to Schauder estimates for the fractional Laplacian
Bucur C.
;
2017
Abstract
We present an elementary approach for the proof of Schauder estimates for the equation (−Δ)su(x) = f(x), 0 < s < 1, with f having a modulus of continuity ωf, based on the Poisson representation formula and dyadic ball approximation argument. We give the explicit modulus of continuity of u in balls Br(x) ⊂ Rn in terms of ωf.
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