Translator Disclaimer
2018 Global results for eikonal Hamilton–Jacobi equations on networks
Antonio Siconolfi, Alfonso Sorrentino
Anal. PDE 11(1): 171-211 (2018). DOI: 10.2140/apde.2018.11.171

Abstract

We study a one-parameter family of eikonal Hamilton–Jacobi equations on an embedded network, and prove that there exists a unique critical value for which the corresponding equation admits global solutions, in a suitable viscosity sense. Such a solution is identified, via a Hopf–Lax-type formula, once an admissible trace is assigned on an intrinsic boundary. The salient point of our method is to associate to the network an abstract graph, encoding all of the information on the complexity of the network, and to relate the differential equation to a discrete functional equation on the graph. Comparison principles and representation formulae are proven in the supercritical case as well.

Citation

Download Citation

Antonio Siconolfi. Alfonso Sorrentino. "Global results for eikonal Hamilton–Jacobi equations on networks." Anal. PDE 11 (1) 171 - 211, 2018. https://doi.org/10.2140/apde.2018.11.171

Information

Received: 5 December 2016; Revised: 25 May 2017; Accepted: 10 August 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 1377.35250
MathSciNet: MR3707295
Digital Object Identifier: 10.2140/apde.2018.11.171

Subjects:
Primary: 35F21, 35R02
Secondary: 35B51, 49L25

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
41 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.11 • No. 1 • 2018
MSP
Back to Top