Viscosity solutions of Eikonal equations on topological networks

Details Viscosity solutions of Eikonal equations on topological networks Viscosity solutions of Eikonal equations on topological networks

2011-03-21

arxiv.org/abs/1103.4041v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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