Viscosity solutions of Eikonal equations on topological networks
Viscosity solutions for eikonal equations on topological networks — existence via representation formulas and uniqueness via comparison principle. With Fabio Camilli, 2012.
Authors: Dirk Schieborn, Fabio Camilli
Journal: Calculus of Variations and Partial Differential Equations
Reference: Calc. Var. DOI 10.1007/s00526-012-0498-z · Preprint on ArXiv
Year of publication: 2012
Abstract
In this paper we introduce a notion of viscosity solutions for eikonal equations on topological networks. The existence of a solution to the Dirichlet problem is derived via representation formulas that employ a distance function associated with the Hamiltonian. A comparison theorem, based on Ishii’s classical argument, yields the uniqueness of the solution.