In this paper we study the asymptotic behavior of solutions to the subelliptic p-Poisson equation as p -> +infinity in Carnot-Caratheodory spaces. In particular, introducing a suitable notion of differentiability, extend the celebrated result of Bhattacharya et al. (Rend Sem Mat Univ Politec Torino Fascicolo Speciale 47:15-68, 1989) and we prove that limits of such solutions solve in the sense of viscosity a hybrid first and second order PDE involving the infinity-Laplacian and the Eikonal equation.
The asymptotic p-Poisson equation as p→ ∞ in Carnot-Carathéodory spaces
Verzellesi S.
2024
Abstract
In this paper we study the asymptotic behavior of solutions to the subelliptic p-Poisson equation as p -> +infinity in Carnot-Caratheodory spaces. In particular, introducing a suitable notion of differentiability, extend the celebrated result of Bhattacharya et al. (Rend Sem Mat Univ Politec Torino Fascicolo Speciale 47:15-68, 1989) and we prove that limits of such solutions solve in the sense of viscosity a hybrid first and second order PDE involving the infinity-Laplacian and the Eikonal equation.
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