Published Paper

Inserted: 21 jul 2022
Last Updated: 5 jan 2024

Journal: J. Geom. Anal.
Volume: 33
Number: 3
Pages: Art. 77
Year: 2023
Doi: 10.1007/s12220-022-01124-6

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 $\mathbb{H}^n$. Amongst other results, we prove that the weak solutions to such a class of problems are bounded and H\"older continuous, by also establishing general estimates as fractional Caccioppoli-type estimates with tail and logarithmic-type estimates.

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• Manfredini-Palatucci-Piccinini-Polidoro_Holder-continuity_ArXiv.pdf