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A general compactness theorem for shape/geometric analysis and optimization is given for a family of subsets verifying the uniform fat segment property in a bounded open holdall with or without constraints on the De Giorgi (11) or the γ-density perimeter of Bucur and Zolesio (3). The uniform fat...
Semilinear elliptic partial differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. These results are applied to a stochastic optimal control problem with infinite horizon. Applications to controlled stochastic heat and wave equations are given.
We obtain error bounds for monotone approximation schemes of a stochastic impulse control problem. This is an extension of the theory for error estimates for the Hamilton-Jacobi-Bellman equation. We obtain almost the same estimate on the rate of convergence as in the equation without impulsions...
Optimal stopping and impulse control problems with certain multiplicative functionals are considered. The stopping problems are solved by showing the unique existence of the solutions of relevant variational inequalities. However, since functions defining the multiplicative costs change the...
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