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arXiv · 2608.09051

On the Schauder Estimates for Non-local Equations with Drift: The Supercritical Case

Yanfang Li·Guohuan Zhao
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Abstract

We establish a Schauder estimate for a nonlocal Cauchy problem with drift. The leading operator is the generator of a non-degenerate $\alpha$-stable process with $\alpha\in(0,1)$, and the drift is $\beta$-H\"older continuous with $\beta \in (1-\alpha,1)$. The proof relies on a refined conic Littlewood--Paley decomposition and a one-dimensional one-sided dyadic maximum principle.

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Yanfang Li, Guohuan Zhao. 2026-08-10. On the Schauder Estimates for Non-local Equations with Drift: The Supercritical Case. https://arxiv.org/abs/2608.09051

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