# American Institute of Mathematical Sciences

June  2008, 21(2): 513-535. doi: 10.3934/dcds.2008.21.513

## Uniqueness results for boundary value problems arising from finite fuel and other singular and unbounded stochastic control problems

 1 Dipartimento di Matematica Pura ed Applicata, Via Trieste, 63, 35121 Padova 2 Dipartimento di Metodi e Modelli Matematici, per le Scienze Applicate, Via Trieste, 63, 35121 Padova

Received  January 2007 Revised  December 2007 Published  March 2008

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).
Citation: Monica Motta, Caterina Sartori. Uniqueness results for boundary value problems arising from finite fuel and other singular and unbounded stochastic control problems. Discrete and Continuous Dynamical Systems, 2008, 21 (2) : 513-535. doi: 10.3934/dcds.2008.21.513
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