2026/07/20 by Simone Ciani, Kenta Nakamura
#math.AP
We carry on a study of the point-wise regularity theory for the nonlocal Trudinger equation, with measurable and bounded singular kernel. We establish refined quantitative upper bounds, weak and strong parabolic Harnack inequalities, both under optimal tail conditions. Our analysis relies on the adaptation of a refined De Giorgi-Moser machinery based on the parabolic approach á la Di Benedetto, specifically designed to overcome the technical intricacies of the nonlocal, doubly nonlinear framework.