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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
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