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.
Citation
Yasuhiro Fujita. "Hessian estimates for viscous Hamilton-Jacobi equations with the Ornstein-Uhlenbeck operator." Differential Integral Equations 18 (12) 1383 - 1396, 2005. https://doi.org/10.57262/die/1356059716
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