The Bilateral Minimal Time Function
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 s...
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| Format: | article |
| Published: |
2006
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| Online Access: | http://hdl.handle.net/10725/3447 https://www.heldermann.de/JCA/JCA13/JCA131/jca13005.htm |
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| Summary: | 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. |
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