English

Viscosity solutions of Eikonal equations on topological networks

Analysis of PDEs 2011-03-22 v1

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.

Cite

@article{arxiv.1103.4041,
  title  = {Viscosity solutions of Eikonal equations on topological networks},
  author = {D. Schieborn and F. Camilli},
  journal= {arXiv preprint arXiv:1103.4041},
  year   = {2011}
}
R2 v1 2026-06-21T17:42:25.402Z