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.
Viscosity solutions of Eikonal equations on topological networks / Dirk, Schieborn; Camilli, Fabio. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 46:3-4(2013), pp. 671-686. [10.1007/s00526-012-0498-z]
Viscosity solutions of Eikonal equations on topological networks
CAMILLI, FABIO
2013
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.File allegati a questo prodotto
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