Almost classical solutions of Hamilton-Jacobi equations

Robert Deville, Jesús A. Jaramillo

Research output: Contribution to journalArticlepeer-review


We study the existence of everywhere differentiable functions which axe almost everywhere solutions of quite general Hamilton-Jacobi equations on open subsets of ℝ d or on d-dimensional manifolds whenever d ≥ 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 || ▽u(x)|| x = 1 almost everywhere on M.

Original languageEnglish (US)
Pages (from-to)989-1010
Number of pages22
JournalRevista Matematica Iberoamericana
Issue number3
StatePublished - 2008


  • Almost everywhere solutions
  • Eikonal equation on manifolds
  • Hamilton-Jacobi equations

ASJC Scopus subject areas

  • Mathematics(all)


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