Viscosity solutions of Eikonal equations on topological networks

Viscosity solutions of Eikonal equations on topological networks

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...

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Veröffentlicht in:Calculus of variations and partial differential equations 2013-03, Vol.46 (3-4), p.671-686
Hauptverfasser: Schieborn, Dirk, Camilli, Fabio
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Analysis of PDEs
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Dirichlet problem
Eikonal equation
Mathematical analysis
Mathematical and Computational Physics
Mathematical problems
Mathematics
Mathematics and Statistics
Networks
Partial differential equations
Representations
Systems Theory
Theoretical
Topological manifolds
Topology
Uniqueness
Viscosity
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Beschreibung
Zusammenfassung: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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-012-0498-z