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Journal Articles Calculus of Variations and Partial Differential Equations Year : 2013

Viscosity solutions of Eikonal equations on topological networks

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.

Dates and versions

hal-00724761 , version 1 (22-08-2012)

Identifiers

Cite

D. Schieborn, Fabio Camilli. Viscosity solutions of Eikonal equations on topological networks. Calculus of Variations and Partial Differential Equations, 2013, 46 (3-4), pp.671-686. ⟨10.1007/s00526-012-0498-z⟩. ⟨hal-00724761⟩
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