Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control
نویسنده
چکیده
We study the partial differential equation max {Lu− f,H(Du)} = 0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for HamiltonJacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Hölder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution is Lipschitz continuous.
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