Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 1065-1083

EXISTENCE AND UNIQUENESS RESULTS FOR LINEAR SECOND-ORDER EQUATIONS IN THE HEISENBERG GROUP

Pablo Ochoa and Julio Alejo Ruiz

Universidad Nacional de Cuyo-CONICET
5500 Mendoza, Argentina; ochopablo 'at' gmail.com

Universidad Nacional de Cuyo-CONICET
5500 Mendoza, Argentina; julioalejoruiz 'at' gmail.com

Abstract. 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.

2010 Mathematics Subject Classification: Primary 35R03, 49L25, 35B51.

Key words: Partial differential equations on the Heisenberg group, viscosity solutions, comparison principle.

Reference to this article: P. Ochoa and J. A. Ruiz: Existence and uniqueness results for linear second-order equations in the Heisenberg group. Ann. Acad. Sci. Fenn. Math. 42 (2017), 1065-1083.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4264