Bounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations, and Shape-From-Shading

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dc.creatorMalisoff, Michael
dc.date2003-11-16
dc.date.accessioned2026-07-07T06:21:48Z
dc.date.available2026-07-07T06:21:48Z
dc.descriptionWe study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique bounded-from-below viscosity solution of the Hamilton-Jacobi equation which is null on the target. The result applies to problems with the property that all trajectories satisfying a certain integral condition must stay in a bounded set. We allow problems for which the Lagrangian is not uniformly bounded below by positive constants, in which the hypotheses of the known uniqueness results for Hamilton-Jacobi equations are not satisfied. We apply our theorems to eikonal equations from geometric optics, shape-from-shading equations from image processing, and variants of the Fuller Problem.
dc.description29 pages, 0 figures, accepted for publication in NoDEA Nonlinear Differential Equations and Applications on July 29, 2002
dc.identifierhttps://arxiv.org/abs/math/0311269
dc.identifierhttp://arxiv.org/abs/math/0311269
dc.identifierNoDEA Nonlinear Differential Equations and Applications, Volume 11, Number 1, pp. 95-122, February 2004
dc.identifierdoi:10.1007/s00030-003-1051-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95717
dc.subjectOptimization and Control
dc.subject35F20, 49L25
dc.titleBounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations, and Shape-From-Shading
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