Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications

Francesca da Lio (1) , Olivier Ley (2, 3)

1 Dipartimento di Matematica Pura e Applicata [Padova]
2 LMPT - Laboratoire de Mathématiques et Physique Théorique
3 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we characterize the value function of a finite horizon stochastic control problem with unbounded controls as the unique viscosity solution of the corresponding dynamic programming equation.

Mots clés: degenerate parabolic equations; nonlinear Hamilton-Jacobi equations; nonlinear Isaacs equations; viscosity solutions; unbounded solutions; maximum principle; Linear Quadratic problems.; Linear Quadratic problems

Domaines: Equations aux dérivées partielles [math.AP]

Francesca da Lio, Olivier Ley. Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications. SIAM Journal on Control and Optimization, 2006, 45 (1), pp.74-106. ⟨10.1137/S0363012904440897⟩. ⟨hal-00455993⟩