Existence and uniqueness results for linear second-order equations in the Heisenberg group. (English) Zbl 1430.35234
Summary: In this manuscript, we prove uniqueness and existence results of viscosity solutions for a class of linear second-order equations in the Heisenberg group. We state uniqueness by proving a comparison result to our class of equations, and existence via an application of Perron’s method adapted to our framework. We also provide the explicit construction of the appropriate sub- and supersolutions employed by Perron’s method for a variety of domains in the Heisenberg group.
MSC:
35R03 | PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. |
35B51 | Comparison principles in context of PDEs |
35D40 | Viscosity solutions to PDEs |
49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |