Semigeodesics and the minimal time function
Computer Science and Mathematics Division, Lebanese American University, Byblos Campus, P.O. Box 36, Byblos, Lebanon; email@example.com This paper was written while the author was an ATER at Institut Girard Desargues, Université Lyon I.
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.
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