SIAM Journal on Control and Optimization, Vol.45, No.1, 74-106, 2006
Uniqueness results for second-order Bellman-Isaacs equations under quadratic growth assumptions and applications
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.
Keywords:degenerate parabolic equations;nonlinear Hamilton;Jacobi equations;nonlinear Isaacs equations;viscosity solutions;unbounded solutions;maximum principle;linear quadratic problems