Differentiability of the transition semigroup of the stochastic Burgers equations, and application to the corresponding Hamilton-Jacobi equation
type: Item
instance of: scholarly article
title: Differentiability of the transition semigroup of the stochastic Burgers equations, and application to the corresponding Hamilton-Jacobi equation
zbMATH Open document ID: 0931.37036
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2000-03-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 37L55
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 70H20
Mathematics Subject Classification ID: 37N35
zbMATH DE Number: 1322983
zbMATH Keywords: transition semigroup
zbMATH Keywords: Burger's equation
zbMATH Keywords: Hamilton-Jacobi equation
zbMATH Keywords: fixed point theorem
zbMATH Keywords: optimal control
author: Guiseppe Da Prato
author: A. Debussche
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1322983