JournalsrmiVol. 24, No. 3pp. 989–1010

Almost classical solutions of Hamilton-Jacobi equations

  • Robert Deville

    Université de Bordeaux I, Talence, France
  • Jesús A. Jaramillo

    Universidad Complutense de Madrid, Spain
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Abstract

We study the existence of everywhere differentiable functions which are almost everywhere solutions of quite general Hamilton-Jacobi equations on open subsets of Rd\mathbb R^d or on dd-dimensional manifolds whenever d2d\geq 2. In particular, when MM is a Riemannian manifold, we prove the existence of a differentiable function uu on MM which satisfies the Eikonal equation u(x)x=1\Vert \nabla u(x) \Vert_{x}=1 almost everywhere on MM.

Cite this article

Robert Deville, Jesús A. Jaramillo, Almost classical solutions of Hamilton-Jacobi equations. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 989–1010

DOI 10.4171/RMI/564