Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group - Manfredini, Maria; Palatucci, Giampiero; Piccinini, Mirco; Polidoro, Sergio (The Journal of geometric analysis, 2023)
We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional p -Laplacian operator on the Heisenberg-Weyl group H n . Among other results, we prove that the weak solutions to such a class of problems are bounded and Hölder continuous, by also establishing general estimates as fractional Caccioppoli-type estimates with tail and logarithmic-type estimates.