Comparison principle for parabolic equations in the Heisenberg group

Abstract

We define two notions of viscosity solutions to parabolic equations in the Heisenberg group, depending on whether the test functions concern only the past or both the past and the future. We then exploit the Heisenberg geometry to prove a comparison principle for a class of parabolic equations and show the sufficiency of considering the test functions that concern only the past.

Keywords

• Heisenberg group
• viscosity solutions
• parabolic equations.