Regular Solutions of Second-Order Stationary Hamilton-Jacobi Equations
Abstract
We study a second-order stationary Hamilton-Jacobi equation in infinite dimension. This equation is nonlinear and convex with respect to the first-ord- er term. We use properties of a the transition semigroup associated to the linear equation to write the Hamilton-Jacobi equation in integral form and we prove that this solution is the pointwise limit of a uniformly bounded sequence of classical solutions of approximating problems. Finally, the solution is the value function of the associated optimal stochastic control problem. Some examples are given.