Electron. J. Differential Equations, Vol. 2021 (2021), No. 57, pp. 1-22.

Solving singular evolution problems in sub-Riemannian groups via deterministic games

Pablo Ochoa, Julio Alejo Ruiz

Abstract:
In this manuscript, we prove the existence of viscosity solutions to singular parabolic equations in Carnot groups. We develop the analysis by constructing appropriate deterministic games adapted to the algebraic and differential structures of Carnot groups. We point out that the proof of existence does not require a comparison principle and it is based on an Arzela-Ascoli-type theorem.

Submitted November 10, 2020. Published June 23, 2021.
Math Subject Classifications: 35R03, 49L25, 49N70.
Key Words: Carnot group; viscosity solutions; differential games.

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DOI: https://doi.org/10.58997/ejde.2021.57

Pablo Ochoa
Universidad Nacional de Cuyo-CONICET
Parque Gral. San Martín
Mendoza, 5500, Argentina
email: ochopablo@gmail.com
Julio A. Ruiz
Universidad Nacional de Cuyo-CONICET
Parque Gral. San Martín
Mendoza, 5500, Argentina
email: julioalejoruiz@gmail.com

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