In this paper we study the asymptotic behavior of solutions to the subelliptic p-Poisson equation as p→ + ∞ in Carnot-Carathéodory 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 ∞ -Laplacian and the Eikonal equation.
The asymptotic p-Poisson equation as p→ ∞ in Carnot-Carathéodory spaces / Capogna, L.; Giovannardi, G.; Pinamonti, A.; Verzellesi, S.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - 2024:(2024). [10.1007/s00208-024-02805-z]
The asymptotic p-Poisson equation as p→ ∞ in Carnot-Carathéodory spaces
Giovannardi G.;Pinamonti A.
;Verzellesi S.
2024-01-01
Abstract
In this paper we study the asymptotic behavior of solutions to the subelliptic p-Poisson equation as p→ + ∞ in Carnot-Carathéodory 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 ∞ -Laplacian and the Eikonal equation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
