Harnack estimates for nonlocal drift-diffusion equations

2024/02/19 by Naian Liao, Liao, Naian · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2402.11986

openalex publication_date 2024/02/19 · openalex created_date 2024/02/21 · openalex updated_date 2026/07/28

Abstract

A set of pointwise estimates are established for local solutions to nonlocal diffusion equations with a drift term. In particular, our Harnack estimates are the first ones for such equations, and our Hölder regularity refines certain known result in several aspects. The approach is measure theoretical in the spirit of DeGiorgi classes. It yields novel nonlocal weak Harnack estimates in the elliptic case as well.

Cited by

• Nonnegative solutions to nonlocal parabolic equations

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