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

Abstract

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 ${\mathbb{R}}^N\times (0,+\infty )$ 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 H\''older regularizing effect in space following a result of L. C. Evans and M. R. James.

Cited by in corpus (1)

• An Illustrated Guide of the Modern Approaches of Hamilton-Jacobi Equations and Control Problems with Discontinuities