Calculus of Variations and Geometric Measure Theory

L. Capogna - G. Giovannardi - A. Pinamonti - S. Verzellesi

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

created by pinamonti on 07 Feb 2023
modified by verzellesi on 07 Jun 2024


Published Paper

Inserted: 7 feb 2023
Last Updated: 7 jun 2024

Journal: Math. Ann.
Year: 2023


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.