Preprint

Inserted: 20 jul 2023
Last Updated: 20 jul 2023

Year: 2023

Abstract:

In this paper we study Monge solutions to stationary Hamilton–Jacobi equations associated to discontinuous Hamiltonians in the framework of Carnot groups. After showing the equivalence between Monge and viscosity solutions in the continuous setting, we prove existence and uniqueness for the Dirichlet problem, together with a comparison principle and a stability result.

Keywords: Carnot groups, Hamilton-Jacobi equations, Monge solutions, discontinuous Hamiltonians

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• MONGE SOLUTIONS FOR DISCONTINUOUS HAMILTON-JACOBI EQUATIONS.pdf