Uniqueness of solutions for second order Bellman-Isaacs equations with mixed boundary conditions

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October 2008, 20(4): 739-765. doi: 10.3934/dcds.2008.20.739

Uniqueness of solutions for second order Bellman-Isaacs equations with mixed boundary conditions

Monica Motta ^1, and Caterina Sartori ^2,

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

Received December 2006 Revised October 2007 Published January 2008

Abstract
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We investigate the uniqueness of solutions for boundary value problems in bounded and unbounded domains involving nonlinear degenerate second order Bellman-Isaacs equations and mixed boundary conditions (Dirichlet, generalized Dirichlet and state constrained conditions). These boundary value problems arise from exit or stopping time stochastic differential games or optimal control problems with constraints, such as state and integral constraints.

Keywords: stochastic control problems., Degenerate second order Hamilton-Jacobi equations, mixed boundary conditions, viscosity solutions.

Mathematics Subject Classification: Primary: 35B37, 35J70; Secondary: 49L25, 35G9.

Citation: Monica Motta, Caterina Sartori. Uniqueness of solutions for second order Bellman-Isaacs equations with mixed boundary conditions. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 739-765. doi: 10.3934/dcds.2008.20.739

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