Regularity Theory for Nonlocal Equations with General Growth in the Heisenberg Group

We deal with a wide class of generalized nonlocal p-Laplace equations, so-called nonlocal G-Laplace equations, in the Heisenberg framework. Under natural hypotheses on the N-function G, we provide a unified approach to investigate in the spirit of De Giorgi-Nash-Moser theory, some local properties of weak solutions to such kind of problems, involving boundedness, Hölder continuity and Harnack inequality. To this end, an improved nonlocal Caccioppoli-type estimate as the main auxiliary ingredient is exploited several times.