Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control

Details Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control

2011-02-05

arxiv.org/abs/1102.1109v3

Mathematics

Analysis of PDEs

Scientific paper

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 Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Holder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution is Lipschitz continuous.

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