On the regularizing effect for unbounded solutions of first-order Hamilton-Jacobi equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Barles, Guy¹  Chasseigne, Emmanuel¹ 

[1] Univ Tours, Federat Denis Poisson FR CNRS 2964, Lab Math & Phys Theor UMR CNRS 7350, Parc Grandmont, F-37200 Tours, France

关键词: First-order Hamilton-Jacobi Equations;    Viscosity solutions;    Regularizing effects;   

DOI  :  10.1016/j.jde.2016.01.021

来源: Elsevier

【 摘 要 】

We give a simplified proof of regularizing effects for first-order Hamilton-Jacobi Equations of the form u(t) + H(x, t, Du) = 0 in R-N x (0, +infinity) in the case where the idea is to first estimate u(t). As a consequence, we have a Lipschitz regularity in space and time for coercive Hamiltonians and, for hypo-elliptic Hamiltonians, we also have an Holder regularizing effect in space following a result of L.C. Evans and M.R. James. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free