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.

Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group / Manfredini, Maria; Palatucci, Giampiero; Piccinini, Mirco; Polidoro, Sergio. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 33:3(2023), pp. 1-41. [10.1007/s12220-022-01124-6]

Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group

Manfredini, Maria
Membro del Collaboration Group
;
Polidoro, Sergio
Membro del Collaboration Group
2023

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.
2023
9-gen-2023
33
3
1
41
Hölder Continuity and Boundedness Estimates for Nonlinear Fractional Equations in the Heisenberg Group / Manfredini, Maria; Palatucci, Giampiero; Piccinini, Mirco; Polidoro, Sergio. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 33:3(2023), pp. 1-41. [10.1007/s12220-022-01124-6]
Manfredini, Maria; Palatucci, Giampiero; Piccinini, Mirco; Polidoro, Sergio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1294484
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