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 .
Potential theory approach to Schauder estimates for the Fractional Laplacian / C. Bucur, A. Karakhanyan. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - 145:2(2017 Feb), pp. 637-651. [10.1090/proc/13227]
Potential theory approach to Schauder estimates for the Fractional Laplacian
C. Bucur;
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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