Aim of this paper is to extend the work (Ferrari et al. in Discrete Contin. Dyn. Syst. 34, 2779–2793, 2014) to the Carnot group setting. More precisely, we prove that in every Carnot group a function is q−harmonic (here 1 < q < ∞), if and only if it satisfies a particular asymptotic mean value formula.
Fausto Ferrari, Andrea Pinamonti (2015). Characterization by Asymptotic Mean Formulas of q−Harmonic Functions in Carnot Groups. POTENTIAL ANALYSIS, 43(1), 203-227 [10.1007/s11118-014-9430-9].
Characterization by Asymptotic Mean Formulas of q−Harmonic Functions in Carnot Groups
FERRARI, FAUSTO;
2015
Abstract
Aim of this paper is to extend the work (Ferrari et al. in Discrete Contin. Dyn. Syst. 34, 2779–2793, 2014) to the Carnot group setting. More precisely, we prove that in every Carnot group a function is q−harmonic (here 1 < q < ∞), if and only if it satisfies a particular asymptotic mean value formula.File in questo prodotto:
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