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- W4304202507 abstract "We consider a non-local operator $L_{{ alpha}}$ which is the sum of a fractional Laplacian $triangle^{alpha/2} $, $alpha in (0,1)$, plus a first order term which is measurable in the time variable and locally $beta$-Holder continuous in the space variables. Importantly, the fractional Laplacian $Delta^{ alpha/2} $ does not dominate the first order term. We show that global parabolic Schauder estimates hold even in this case under the natural condition $alpha + beta >1$. Thus, the constant appearing in the Schauder estimates is in fact independent of the $L^{infty}$-norm of the first order term. In our approach we do not use the so-called extension property and we can replace $triangle^{alpha/2} $ with other operators of $alpha$-stable type which are somehow close, including the relativistic $alpha$-stable operator. Moreover, when $alpha in (1/2,1)$, we can prove Schauder estimates for more general $alpha$-stable type operators like the singular cylindrical one, i.e., when $triangle^{alpha/2} $ is replaced by a sum of one dimensional fractional Laplacians $sum_{k=1}^d (partial_{x_k x_k}^2 )^{alpha/2}$." @default.
- W4304202507 created "2022-10-11" @default.
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- W4304202507 date "2019-02-07" @default.
- W4304202507 modified "2023-09-23" @default.
- W4304202507 title "Schauder estimates for drifted fractional operators in the supercritical case" @default.
- W4304202507 doi "https://doi.org/10.48550/arxiv.1902.02616" @default.
- W4304202507 hasPublicationYear "2019" @default.
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