We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1<p<\infty$, following the scheme described in \cite{MPR} for the Euclidean case. The new tool that allows us to consider the subelliptic case is a geometric lemma, Lemma \ref{lemma1} below, that relates the directions of the points of maxima and minima of a function on a small subelliptic ball with the unit horizontal gradient of that function.
On the characterization of p-harmonic functions on the Heisenberg group by mean value properties / Fausto Ferrari;Qing Liu;Juan Manfredi. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 34:7(2014), pp. 2779-2793. [10.3934/dcds.2014.34.2779]
On the characterization of p-harmonic functions on the Heisenberg group by mean value properties
FERRARI, FAUSTO;
2014
Abstract
We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1
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