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

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• 作者：Guy Barles ; ^{guy.barles@lmpt.univ-tours.fr" class="auth_mail" title="E-mail the corresponding author} ; ; Emmanuel Chasseigne ^{emmanuel.chasseigne@lmpt.univ-tours.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35F21 ; 35D35 ; 35D40
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 May 2016
• 年：2016
• 卷：260
• 期：9
• 页码：7020-7031
• 全文大小：246 K

文摘

We give a simplified proof of regularizing effects for first-order Hamilton–Jacobi Equations of the form u_t+H(x,t,Du)=0$u_t+H(x,t,Du)=0$ in R^N×(0,+∞)${\mathbb{R}}^N\times (0,+\infty )$ in the case where the idea is to first estimate u_t$u_t$. As a consequence, we have a Lipschitz regularity in space and time for coercive Hamiltonians and, for hypo-elliptic Hamiltonians, we also have an Hölder regularizing effect in space following a result of L.C. Evans and M.R. James.