Document Type
Article
Publication Date
1-1-2004
Abstract
We 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 that 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.
Publication Source (Journal or Book title)
Nonlinear Differential Equations and Applications
First Page
95
Last Page
122
Recommended Citation
Malisoff, M. (2004). Bounded-from-below solutions of the hamilton-Jacobi equation for optimal control problems with exit times: Vanishing lagrangians, eikonal equations, and shape-from-shading. Nonlinear Differential Equations and Applications, 11 (1), 95-122. https://doi.org/10.1007/s00030-003-1051-8
