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Boundary observability and controllability problems for evolution equations governed by PDEs have been greatly studied in the past years. However, the problems were studied on a case-by-case basis, only for some particular types of boundary controls, and, moreover, several unnatural restrictions...
Sufficient optimality conditions for infinite-dimensional optimization problems are derived in a setting that is applicable to optimal control with endpoint constraints and with equality and inequality constraints on the controls. These conditions involve controllability of the system dynamics,...
LetX be a Markov process taking values in a complete, separable metric spaceE and characterized via a martingale problem for an operatorA. We develop a criterion for invariant measures when rangeA is a subset of continuous functions onE. Using this, uniqueness in the class of all positive finite...
We prove a Hölder continuity property of the locally unique solution to a parametric variational inequality without assuming differentiability of the given data.
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