Issue |
ESAIM: COCV
Volume 12, Number 1, January 2006
|
|
---|---|---|
Page(s) | 120 - 138 | |
DOI | https://doi.org/10.1051/cocv:2005032 | |
Published online | 15 December 2005 |
Semigeodesics and the minimal time function
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.
Received:
29
June
2004
Accepted:
25
February
2005
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.
Mathematics Subject Classification: 49J52 / 49L20 / 49L25
Key words: Minimal time function / Hamilton-Jacobi equations / viscosity solutions / minimal trajectories / eikonal equations / monotonicity of trajectories / proximal analysis / nonsmooth analysis.
© EDP Sciences, SMAI, 2006
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