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arXiv · 2302.03532

The asymptotic $p$-Poisson equation as $p \to \infty$ in Carnot-Carath\'eodory spaces

Luca Capogna·Gianmarco Giovannardi·Andrea Pinamonti·Simone Verzellesi
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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 [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 $\infty-$Laplacian and the Eikonal equation.

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Luca Capogna, Gianmarco Giovannardi, Andrea Pinamonti, Simone Verzellesi. 2023-02-07. The asymptotic $p$-Poisson equation as $p \to \infty$ in Carnot-Carath\'eodory spaces. https://arxiv.org/abs/2302.03532

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