Abstract
We establish local regularity properties for the value function of a variational problem arising in the study of small random perturbations of planar dynamical systems. The approach is to characterize the extremals as solutions to a Hamiltonian system, using the usual Legendre transformation. The differential of the value function is described by a certain stable manifold associated with the Hamiltonian system. The existence and smoothness of this stable manifold is obtained from standard results.
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Communicated by S. R. S. Varadhan
Key arguments of this paper were developed while the author was a visitor at the Division of Applied Mathematics of Brown University.
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Day, M.V. Regularity of boundary quasi-potentials for planar systems. Appl Math Optim 30, 79–101 (1994). https://doi.org/10.1007/BF01261992
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DOI: https://doi.org/10.1007/BF01261992