Journal of Convex Analysis 13 (2006), No. 1, 061--080
Copyright Heldermann Verlag 2006
The Bilateral Minimal Time Function
Dept. of Mathematics and Statistics, Concordia University, 1400 De Maisonneuve Boul. West, Montreal, Quebec H3G 1M8, Canada
Permanent Address: Computer Science and Mathematics Division, Lebanese American University, Byblos Campus, Lebanon
We study the minimal time function as a function of two variables (the initial and the terminal points). This function, called the "bilateral minimal time function", plays a central role in the study of the Hamilton-Jacobi equation of minimal control in a domain which contains the target set, as shown in a recent article of F. H. Clarke and the author [J. Convex Analysis 11 (2004) 413--436]. We study the regularity of the function, and characterize it as the unique (viscosity) solution of partial Hamilton-Jacobi equations with certain boundary conditions.
Keywords: Minimal time function, Hamilton-Jacobi equations, viscosity solutions, regularity of value functions, nonsmooth analysis, proximal analysis.
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