https://inria.hal.science/inria-00074041Gozzi, FaustoFaustoGozziRouy, ElisabethElisabethRouyNUMATH - Mathematical Analysis and Numerical Simulation of Non-Linear Models - INRIA Lorraine - Inria - Institut National de Recherche en Informatique et en AutomatiqueRegular Solutions of Second-Order Stationary Hamilton-Jacobi EquationsHAL CCSD1995Hamilton-jacobi equationsoptimal stochastic controldynamic programmingito's formulainfinite dimensionmaximal monotone operators[INFO.INFO-OH] Computer Science [cs]/Other [cs.OH]Inria, Rapport De Recherche2006-05-24 14:22:252023-02-07 03:40:182006-05-31 14:24:28enReportsapplication/pdf1We 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.