2025/08/22 by Simone Ciani, S Ciani, Kenta Nakamura +2
Mathematics · Physics and Astronomy · #Differential Equations and Boundary Problems #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons #math.AP
paper · pdf · doi:10.48550/arxiv.2508.16247
openalex publication_date 2025/08/22 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
We propose a new paradigm for the point-wise regularity theory of parabolic nonlocal problems, by addressing directly the elements of a wide parabolic energy class. First we carry on a refined analysis of their local boundedness under optimal tail conditions, and then prove several weak Harnack estimates through a purely measure-theoretical framework. Then we give a novel proof of the nonlocal parabolic Harnack inequality, that avoids any covering argument or lemma à la John-Nirenberg and is valid regardless of any comparison principle. The regularity program is completed by addressing local Hölder estimates, eventually leading to a Liouville-type theorem.