A new formulation of Harnack?s inequality for nonlocal operators

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Regularity estimates for elliptic nonlocal operators (2015, methodology): “)+c2α(2−α) ˆ Rd\B1 u−(z) (|z|2 −(3 4) 2)α/2|z −y|d dz ≤ cu(y) +cα(2−α) ˆ Rd\B1 u−(z) |z|d+α dz. The proof of the theorem is complete. Note that diﬀerent versions of this result have been announced in [21]. 2The second author would like to use the opportunity to correct an error in [19] concerning th”
Quantitative approximation properties for the fractional heat equation (2017, background): “The maximum principle for example in general only holds on global scales, which does not rule out local oscillations [20, 34].”
On the regularity theory for mixed local and nonlocal quasilinear elliptic equations (2021, methodology): “We refer to Kassmann [32], Castro-Kuusi-Palatucci [16], BrascoLindgren-Schikorra-Strömqvist [9–11], Ding-Zhang-Zhou [21] for the purely nonlocal tail and Garain-Kinnunen [28,29] for the mixed local and nonlocal tail.”