Differentiability of the transition semigroup of the stochastic Burgers equations, and application to the corresponding Hamilton-Jacobi equation
The authors present some estimates on derivatives of the transition semigroup of Burger's equation. These estimates allow the authors to prove existence and uniqueness of a regular solution of the corresponding Hamilton-Jacobi equation. The proof of existence is based on a fixed point theorem in a suitable space of functions having exponential growth. The authors apply this result using a usual argument of dynamic programming to some optimal control problems.
scientific article; zbMATH DE number 1322983