Special Session 1: Analysis of PDEs and Free Boundary Problems

The asymptotic $p$-Poisson equation as $p \\to \\infty$ in Carnot-Caratheodory spaces

Andrea Pinamonti
University of Trento
Italy
Co-Author(s):    Luca Capogna,Gianmarco Giovannardi and Simone Vercellesi
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 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.