Differential and Integral Equations

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

Yasuhiro Fujita

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356059716

Mathematical Reviews number (MathSciNet)
MR2174978

Zentralblatt MATH identifier
1212.35207

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B45: A priori estimates 35K15: Initial value problems for second-order parabolic equations 49L25: Viscosity solutions

Citation

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


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