The asymptotic $p$-Poisson equation as $p \to \infty$ in Carnot-Carath\'eodory spaces
Analysis of PDEs
2023-02-08 v1
Abstract
In this paper we study the asymptotic behavior of solutions to the subelliptic -Poisson equation as in Carnot Carath\'eodory spaces. In particular, introducing a suitable notion of differentiability, we extend the celebrated result of Bhattacharya, DiBenedetto and Manfredi [Rend. Sem. Mat. Univ. Politec. Torino, 1989, Special Issue, 15-68] 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.
Keywords
Cite
@article{arxiv.2302.03532,
title = {The asymptotic $p$-Poisson equation as $p \to \infty$ in Carnot-Carath\'eodory spaces},
author = {Luca Capogna and Gianmarco Giovannardi and Andrea Pinamonti and Simone Verzellesi},
journal= {arXiv preprint arXiv:2302.03532},
year = {2023}
}