The asymptotic p -Poisson equation as p →∞ in Carnot-Carathéodory spaces

In this paper we study the asymptotic behavior of solutions to the subelliptic p -Poisson equation as p→ +∞ 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 ∞ -Laplacian and the Eikonal equation.