Accepted Paper

Inserted: 7 feb 2023
Last Updated: 9 jan 2024

Journal: Mathematische Annalen
Year: 2023

Abstract:

In this paper we study the asymptotic behavior of solutions to the subelliptic $p$-Poisson equation as $p\to +\infty$ in Carnot Carath\'eodory spaces. In particular, introducing a suitable notion of differentiability, we extend the celebrated result of Bhattacharya, DiBenedetto and Manfredi \cite{BDM} and we prove that limits of such solutions solve in the sense of viscosity a hybrid first and second order PDE involving the $\infty-$Laplacian and the Eikonal equation.

Download:

• LastVersion.pdf