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Viscosity solutions of Eikonal equations on topological networks

By D. Schieborn and F. Camilli

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

Topics: Mathematics - Analysis of PDEs, 49L25, 58G20, 35F2
Year: 2011
OAI identifier: oai:arXiv.org:1103.4041
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