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  1. Abstract

    We provide a suitable generalisation of Pansu’s differentiability theorem to general Radon measures on Carnot groups and we show that if Lipschitz maps between Carnot groups are Pansu-differentiable almost everywhere for some Radon measures$$\mu $$μ, then$$\mu $$μmust be absolutely continuous with respect to the Haar measure of the group.

     
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  2. In this paper we study the asymptotic behavior of solutions to the subelliptic p-Poisson equation as $p\to \infty$ in Carnot-Carathéodory spaces. In particular, introducing a suitable notion of differentiability, extend the celebrated result of Bhattacharya et al. (Rend Sem Mat Univ Politec Torino Fascicolo Speciale 47:15–68, 1989) and we prove that limits of such solutions solve in the sense of viscosity a hybrid first and second order PDE involving the infinity- Laplacian and the Eikonal equation. 
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