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

Monica Motta; Caterina Sartori

doi:10.3934/dcds.2008.20.739

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2008, Volume 20, Issue 4: 739-765. Doi: 10.3934/dcds.2008.20.739

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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
2.
Dipartimento di Metodi e Modelli Matematici, per le Scienze Applicate, Via Trieste, 63, 35121 Padova

Received: November 30, 2006

Revised: September 30, 2007

Published: September 2008

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Abstract

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:

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

Mathematics Subject Classification: Primary: 35B37, 35J70; Secondary: 49L25, 35G99.

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