Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups

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.

We added Section 2.2 and we fixed the proof of Proposition 3.3