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

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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
Keywords: minimal time function, Hamilton-Jacobi equations, viscosity solutions, minimal trajectories, eikonal equations, monotonicity of trajectories, proximal analysis, nonsmooth analysis 
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     author = {Nour, Chadi},
     title = {Semigeodesics and the minimal time function},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {120--138},
     publisher = {EDP-Sciences},
     volume = {12},
     number = {1},
     year = {2006},
     doi = {10.1051/cocv:2005032},
     mrnumber = {2192071},
     zbl = {1114.49028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005032/}
}
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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

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