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Almost classical solutions of Hamilton-Jacobi equations


Deville, Robert and Jaramillo Aguado, Jesús Ángel (2008) Almost classical solutions of Hamilton-Jacobi equations. Revista Matemática Iberoamericana, 24 (3). pp. 989-1010. ISSN 0213-2230

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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 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 a on M which satisfies the Eikonal equation parallel to del u(x)parallel to(x) = 1 almost everywhere on M.

Item Type:Article
Uncontrolled Keywords:Riemannian-Manifolds; Gradient Problem; Hamilton-Jacobi Equations; Eikonal Equation On Manifolds; Almost Everywhere Solutions
Subjects:Sciences > Mathematics > Functions
ID Code:16596

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Last Modified:07 Feb 2014 09:32

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