Open Access
November, 2008 Almost classical solutions of Hamilton-Jacobi equations
Robert Deville , Jesús A. Jaramillo
Rev. Mat. Iberoamericana 24(3): 989-1010 (November, 2008).


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 $M$.


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Robert Deville . Jesús A. Jaramillo . "Almost classical solutions of Hamilton-Jacobi equations." Rev. Mat. Iberoamericana 24 (3) 989 - 1010, November, 2008.


Published: November, 2008
First available in Project Euclid: 9 December 2008

zbMATH: 1161.26005
MathSciNet: MR2490207

Primary: 26B05 , 35B65 , 58J32

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

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 3 • November, 2008
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