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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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Abstract

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
References:

D. Azagra, J. Ferrera and F. López-Mesas, Nonsmooth analysis and Hamilton-Jacobi equations on Riemannian manifolds. J. Funct. Anal. 220 (2005) 304–361.

G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi. Mathématiques el Applications, 17, Springer-Verlag (1994).

M. T. Benameur, Triangulations and the stability theorem for foliations. Pacific J. of Math. 179 (1997) 221–239.

Z. Buczolich, Solution to the gradient problem of C. E. Weil. Revista. Mat. Iberoamericana 21 (2005) 889–910.

M. G. Crandall, H. Ishii and P. L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27 (1992) 1–67.

R. Deville and É. Matheron, Infinite games, Banach space geometry and the eikonal equation. To appear in Proc. London Math. Soc.

J. Malý, M. Zelený, A note on Buczolich’s solution of the Weil gradient problem. Preprint.

C. Mantegazza and A. C. Mennucci, Hamilton-Jacobi Equations and Distance Functions on

Riemannian Manifods. Appl. Math. and Optim. 47 (2003) 1–25.

C. E. Weil, On properties of derivatives. Trans. Amer. Math. Soc. 114 (1965) 363–376.

H. Whitney, Geometric integration theory. Princeton Univ. Press, 19 (1957).

Deposited On:03 Oct 2012 08:22
Last Modified:07 Feb 2014 09:32

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