Viscosity solutions of Eikonal equations on topological networks
Dirk Schieborn, Fabio Camilli · arXiv (Cornell University) · 2011
In this paper we introduce a notion of viscosity solutions for Eikonal equations defined on topological networks. Existence of a solution for the Dirichlet problem is obtained via representation formulas involving a distance function associated to the Hamiltonian. A comparison theorem based on Ishii's classical argument yields the uniqueness of the solution.