Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 57, pp. 1-22.

Title: Solving singular evolution problems in sub-Riemannian groups via deterministic games
       
Authors: Pablo Ochoa      (Univ. Nacional de Cuyo, Mendoza, Argentina)
         Julio Alejo Ruiz (Univ. Nacional de Cuyo, Mendoza, Argentina)

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.