We study the existence of everywhere differentiable functions which are almost everywhere solutions of quite general Hamilton-Jacobi equations on open subsets of or on -dimensional manifolds whenever . In particular, when is a Riemannian manifold, we prove the existence of a differentiable function on which satisfies the Eikonal equation almost everywhere on .
Cite this article
Robert Deville, Jesús A. Jaramillo, Almost classical solutions of Hamilton-Jacobi equations. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 989–1010DOI 10.4171/RMI/564