Revista Matemática Iberoamericana

Almost classical solutions of Hamilton-Jacobi equations

Robert Deville and Jesús A. Jaramillo

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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 $\mathbb R^d$ 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

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

Dates
First available in Project Euclid: 9 December 2008

Permanent link to this document
http://projecteuclid.org/euclid.rmi/1228834302

Zentralblatt MATH identifier
1161.26005

Mathematical Reviews number (MathSciNet)
MR2490207

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

Keywords
Hamilton-Jacobi equations eikonal equation on manifolds almost everywhere solutions

Citation

Deville , Robert; Jaramillo , Jesús A. Almost classical solutions of Hamilton-Jacobi equations. Rev. Mat. Iberoamericana 24 (2008), no. 3, 989--1010. http://projecteuclid.org/euclid.rmi/1228834302.


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