Abstract
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 $M$.
Citation
Robert Deville . Jesús A. Jaramillo . "Almost classical solutions of Hamilton-Jacobi equations." Rev. Mat. Iberoamericana 24 (3) 989 - 1010, November, 2008.
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