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Semigeodesics and the minimal time function

Published online by Cambridge University Press:  15 December 2005

Chadi Nour
Chadi Nour*
Affiliation:
Computer Science and Mathematics Division, Lebanese American University, Byblos Campus, P.O. Box 36, Byblos, Lebanon; cnour@lau.edu.lb This paper was written while the author was an ATER at Institut Girard Desargues, Université Lyon I.
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Abstract

We study the Hamilton-Jacobi equation of the minimal time function in a domain which contains the target set. We generalize the results of Clarke and Nour [J. Convex Anal., 2004], where the target set is taken to be a single point. As an application, we give necessary and sufficient conditions for the existence of solutions to eikonal equations.

Keywords

Minimal time functionHamilton-Jacobi equationsviscosity solutionsminimal trajectorieseikonal equationsmonotonicity of trajectoriesproximal analysisnonsmoothanalysis.

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 1 , January 2006 , pp. 120 - 138
Copyright
© EDP Sciences, SMAI, 2006

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