A comparison principle for singular parabolic equations in the Heisenberg group

Abstract

In this work, we prove a comparison principle for singular parabolic equations with boundary conditions in the context of the Heisenberg group. In particular, this result applies to interesting equations, such as the parabolic infinite Laplacian, the mean curvature flow equation and more general homogeneous diffusions.

Keywords

• Partial differential equations on the Heisenberg group
• viscosity solutions