We establish uniqueness of viscosity solutions for some boundary value problems arising from stochastic optimal control problems with unbounded, possibly singular, controls. They involve a nonlinear degenerate second order Bellman-Isaacs equation and mixed boundary conditions (Dirichlet, generalized Dirichlet and state constrained conditions).
Uniqueness of solutions for second order Bellman-Isaacs equations with mixed boundary conditions
SARTORI, CATERINA;MOTTA, MONICA
2008
Abstract
We establish uniqueness of viscosity solutions for some boundary value problems arising from stochastic optimal control problems with unbounded, possibly singular, controls. They involve a nonlinear degenerate second order Bellman-Isaacs equation and mixed boundary conditions (Dirichlet, generalized Dirichlet and state constrained conditions).
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