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monotonicity of trajectories

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Semigeodesics and the minimal time function
Chadi Nour
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 12 / Issue 1 / January 2006

Published online by Cambridge University Press:

15 December 2005, pp. 120-138

Print publication:

January 2006
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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.