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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.
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https://hal.inria.fr/hal-00724761
Contributor : Estelle Bouzat Connect in order to contact the contributor
Submitted on : Wednesday, August 22, 2012 - 3:26:45 PM
Last modification on : Wednesday, November 3, 2021 - 2:18:08 PM

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

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