Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I : regularity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 3, pp. 426-451.

We formulate an Hamilton-Jacobi partial differential equation

H(x,Du(x))=0
on a n dimensional manifold M, with assumptions of convexity of H(x,·) and regularity of H (locally in a neighborhood of {H=0} in T * M); we define the “min solution” u, a generalized solution; to this end, we view T * M as a symplectic manifold. The definition of “min solution” is suited to proving regularity results about u; in particular, we prove in the first part that the closure of the set where u is not regular may be covered by a countable number of n-1 dimensional manifolds, but for a n-1 negligeable subset. These results can be applied to the cutlocus of a C 2 submanifold of a Finsler manifold.

DOI : 10.1051/cocv:2004014
Classification : 49L25, 53C22, 53C60
Mots clés : Hamilton-Jacobi equations, conjugate points
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     title = {Regularity and variationality of solutions to {Hamilton-Jacobi} equations. {Part} {I} : regularity},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {426--451},
     publisher = {EDP-Sciences},
     volume = {10},
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     mrnumber = {2084331},
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Mennucci, Andrea C. G. Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I : regularity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 3, pp. 426-451. doi : 10.1051/cocv:2004014. http://www.numdam.org/articles/10.1051/cocv:2004014/

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