Semigeodesics and the minimal time function
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 120-138.

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.

DOI : 10.1051/cocv:2005032
Classification : 49J52, 49L20, 49L25
Mots-clés : minimal time function, Hamilton-Jacobi equations, viscosity solutions, minimal trajectories, eikonal equations, monotonicity of trajectories, proximal analysis, nonsmooth analysis 
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     title = {Semigeodesics and the minimal time function},
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     pages = {120--138},
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     volume = {12},
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Nour, Chadi. Semigeodesics and the minimal time function. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 120-138. doi : 10.1051/cocv:2005032. http://www.numdam.org/articles/10.1051/cocv:2005032/

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