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We study a one-dimensional variational problem with two or more level set constraints. The existence of global and local minimizers turns out to be dependent on the regularity of the energy density. A complete characterization of local minimizers and the underlying energy landscape is provided....
This paper is devoted to the autonomous Lagrange problem of the calculus of variations with a discontinuous Lagrangian. We prove that every minimizer is Lipschitz continuous if the Lagrangian is coercive and locally bounded. The main difference with respect to the previous works in the...
We study the variational inequality associated with a bounded-velocity control problem when discretionary stopping is allowed. We establish the existence of a strong solution by using the viscosity solution techniques. The optimal policy is shown to exist from the optimality conditions in the...
We introduce a generalized Wiener measure associated with a Gaussian Markov process and define a generalized analytic operator-valued function space integral as a bounded linear operator from L
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