I will talk about a joint result with Gianmarco Giovannardi, Andrea Pinamonti and Simone Verzellesi, concerning 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, we extend the celebrated result of Bhattacharya, DiBenedetto and Manfredi 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.
