Calculus of Variations and Geometric Measure Theory

M. Manfredini - G. Palatucci - M. Piccinini - S. Polidoro

Hölder continuity and boundedness estimates for nonlinear fractional equations in the Heisenberg group

created by piccinini on 21 Jul 2022
modified by palatucci on 05 Jan 2024


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

ArXiv: 2207.03741v2 PDF


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.