On some nonlinear degenerate elliptic equations arising in stochastic control

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari
Ore 16:30

Relatore:

• Martino Bardi (Università di Padova)

Abstract:

The talk is on a joint work with Annalisa Cesaroni and Luca Rossi. We consider a class of Bellman equations in bounded domains where the ellipticity of the operator degenerates at the boundary. We prove that sub- and supersolutions whose growth at the boundary is suitably controlled must be constant. We apply this result to two problems of optimal control for the diffusion process associated to the Bellman operator. In the first problem the cost is a function of the exit point of the process from the domain. The second problem is a small discount limit related with ergodic control with state constraints.

Referente: Fabio Bagagiolo