Revista Matemática Iberoamericana

Almost classical solutions of Hamilton-Jacobi equations

Robert Deville and Jesús A. Jaramillo

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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 $M$.

Article information

Rev. Mat. Iberoamericana, Volume 24, Number 3 (2008), 989-1010.

First available in Project Euclid: 9 December 2008

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Primary: 26B05: Continuity and differentiation questions 35B65: Smoothness and regularity of solutions 58J32: Boundary value problems on manifolds

Hamilton-Jacobi equations eikonal equation on manifolds almost everywhere solutions


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

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