Lower estimates of L∞-norm of gradients for Cauchy problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:458

Article

Fujita, Yasuhiro¹ 

[1] Univ Toyama, Dept Math, Toyama 9308555, Japan

关键词: Lipschitz constants;    Lower estimates;    Optimality;    Parabolic equations;    Hamilton Jacobi equations;    Logarithmic Sobolev inequality;   

DOI  :  10.1016/j.jmaa.2017.08.045

来源: Elsevier

【 摘 要 】

In this paper, we consider the Cauchy problems for a uniformly parabolic equation and a Hamilton-Jacobi equation. Our aim is to show the optimality of an upper estimate of the L-infinity-norm of the gradient of solution to each Cauchy problem. In order to achieve this aim, we investigate a lower estimate of this L-infinity-norm. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free