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Manfredini, Maria; Palatucci, Giampiero; Piccinini, Mirco; Polidoro, Sergio, (2023)  - Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group  - THE JOURNAL OF GEOMETRIC ANALYSIS, Articolo su rivista - Articolo in rivista (262) (, , ) - pagg. 1 - 41

Abstract: 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 Hn. 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.