Special Session 70: Progress and Challenges in Nonlocal and Nonhomogeneous PDEs

On the weak Harnack inequality for a generalized Orlicz De Giorgi class
simone ciani
University of Bologna Alma Mater
Italy
Co-Author(s):    Eurica Henriques, Igor I. Skrypnik
Abstract:
We introduce a generalization of De Giorgi classes with Orlicz growth. The aim is twofold: on the one hand, to encompass a broader class of functionals and equations; on the other hand, to provide a definition based on a simple energy inequality that does not rely on an underlying functional, but rather on the intrinsic scaling between radii and levels. For these classes, we establish a Weak Harnack inequality, thereby unifying its validity across non-uniformly elliptic equations, double-phase and degenerate double-phase functionals, as well as functionals with variable exponents.