We study the existence of everywhere differentiable functions
which are almost everywhere solutions of quite general
Hamilton-Jacobi equations on open subsets of $\mathbb R^d$ or on
$d$-dimensional manifolds whenever $d\geq 2$. In particular,
when $M$ is a Riemannian manifold, we prove the existence of a
differentiable function $u$ on $M$ which satisfies the Eikonal
equation $\Vert \nabla u(x) \Vert_{x}=1$ almost everywhere on $M$.
Publié le : 2008-04-15
Classification:
Hamilton-Jacobi equations,
eikonal equation on manifolds,
almost everywhere solutions,
26B05,
35B65,
58J32
@article{1228834302,
author = {Deville
,
Robert and Jaramillo
,
Jes\'us A.},
title = {Almost classical solutions of Hamilton-Jacobi equations},
journal = {Rev. Mat. Iberoamericana},
volume = {24},
number = {2},
year = {2008},
pages = { 989-1010},
language = {en},
url = {http://dml.mathdoc.fr/item/1228834302}
}
Deville
,
Robert; Jaramillo
,
Jesús A. Almost classical solutions of Hamilton-Jacobi equations. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp. 989-1010. http://gdmltest.u-ga.fr/item/1228834302/