Hessian estimates for viscous Hamilton-Jacobi equations with the Ornstein-Uhlenbeck operator. (English) Zbl 1212.35207
Summary: 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 S. N. Kruzhkov. On the other hand, our lower estimate on the Hessian matrix of solutions is best possible in some sense.
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
