Differential and Integral Equations
- Differential Integral Equations
- Volume 18, Number 12 (2005), 1383-1396.
Hessian estimates for viscous Hamilton-Jacobi equations with the Ornstein-Uhlenbeck operator
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 . On the other hand, our lower estimate on the Hessian matrix of solutions is best possible in some sense.
Differential Integral Equations, Volume 18, Number 12 (2005), 1383-1396.
First available in Project Euclid: 21 December 2012
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Fujita, Yasuhiro. Hessian estimates for viscous Hamilton-Jacobi equations with the Ornstein-Uhlenbeck operator. Differential Integral Equations 18 (2005), no. 12, 1383--1396. https://projecteuclid.org/euclid.die/1356059716