A Liouville type result for a degenerate Bellman operator in a bounded domain
Martino Bardi, Annalisa Cesaroni, Luca Rossi · arXiv (Cornell University) · 2015
We derive a Liouville type result for a Bellman operator in a bounded smooth domain. The ellipticity of the operator is assumed to degenerate at the boundary and a condition involving also the drift is further imposed. We apply this result to stochastic control problems, in particular to an exit problem and to the small discount limit related with ergodic control with state constraints. In this context, our condition on the behavior of the operator near the boundary ensures some invariance property of the domain for the associated controlled diffusion process