A PDE approach to large deviations for stochastic PDE with Levy noise

We will present a large deviation principle result for solutions of abstract stochastic evolution equations with small Levy noise. The result is obtained by a combination of PDE and probabilistic techniques. The key component of this approach is the use of Hamilton-Jacobi-Bellman integro-partial differential equations in Hilbert spaces. We will discuss the notion of
viscosity solution for such infinite dimensional integro-PDE.