Viscosity solutions of Eikonal equations on topological networks
Analysis of PDEs
2011-03-22 v1
Abstract
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.
Cite
@article{arxiv.1103.4041,
title = {Viscosity solutions of Eikonal equations on topological networks},
author = {D. Schieborn and F. Camilli},
journal= {arXiv preprint arXiv:1103.4041},
year = {2011}
}