We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlin- ear 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.
Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group / Manfredini, Maria; Palatucci, Giampiero; Piccinini, Mirco; Polidoro, Sergio. - In: JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1559-002X. - 33:(2023), pp. 77.1-77.41. [10.1007/s12220-022-01124-6]
Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group
Giampiero Palatucci
;Mirco Piccinini;
2023-01-01
Abstract
We extend the celebrate De Giorgi-Nash-Moser theory to a wide class of nonlin- ear 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
