Differential and Integral Equations

Hessian estimates for viscous Hamilton-Jacobi equations with the Ornstein-Uhlenbeck operator

Yasuhiro Fujita

Abstract

In this paper, we consider Hessian estimates of solutions of the Cauchy problem for parabolic PDEs with the Ornstein-Uhlenbeck operator. Our upper estimate on the Hessian matrix of solutions is a generalization of the result of Kružkov [4]. On the other hand, our lower estimate on the Hessian matrix of solutions is best possible in some sense.

Article information

Source
Differential Integral Equations, Volume 18, Number 12 (2005), 1383-1396.

Dates
First available in Project Euclid: 21 December 2012