- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:45
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
24
2008
3
Almost classical solutions of Hamilton-Jacobi equations
Robert
Deville
Université de Bordeaux I, TALENCE CEDEX, FRANCE
Jesús
Jaramillo
Universidad Complutense de Madrid, MADRID, SPAIN
Hamilton-Jacobi equations, eikonal equation on manifolds, almost everywhere solutions
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 $M$.
Real functions
Partial differential equations
Global analysis, analysis on manifolds
General
989
1010
10.4171/RMI/564
http://www.ems-ph.org/doi/10.4171/RMI/564