Gozzi, Fausto Regularity of solutions of a second order Hamilton-Jacobi equation and application to a control problem. (English) Zbl 0842.49021 Commun. Partial Differ. Equations 20, No. 5-6, 775-826 (1995). A certain Hamilton-Jacobi equation on a Hilbert space with initial conditions is thoroughly studied and existence and regularity results are established. Then the results are applied to solve a certain stochastic optimal control problem. The solution to the Hamilton-Jacobi equation turns out to be the value function of the optimal control problem. To solve the Hamilton-Jacobi equation, a linearized version is solved first. This can be done by using known techniques. The resulting semigroup is then used to write an integral version of the Hamilton-Jacobi equation and then its solution follows by a fixed point argument. The results are of interest in functional analysis, probability, and stochastic optimal control. Reviewer: H.Cendra (Bahia Blanca) Cited in 1 ReviewCited in 39 Documents MSC: 49L99 Hamilton-Jacobi theories 49N60 Regularity of solutions in optimal control 70H20 Hamilton-Jacobi equations in mechanics 93E20 Optimal stochastic control Keywords:parabolic equations; Hamilton-Jacobi equation on a Hilbert space; regularity; stochastic optimal control problem; value function PDFBibTeX XMLCite \textit{F. Gozzi}, Commun. Partial Differ. Equations 20, No. 5--6, 775--826 (1995; Zbl 0842.49021) Full Text: DOI