Eikonal equations with discontinuities
Eikonal equations with discontinuities
This paper is concerned with the Hamilton-Jacobi equation of eikonal type $$ H(Du)=n(x) \qquad x\in \Omega \subset {\Bbb R}^N ,\tag E $$ where $H$ is convex, $Du$ represents the gradient of $u$ with respect to $x$, and $n(x)$ is lower semi-continuous. In this work, a new notion of generalized solution …