# Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I: Regularity

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 10, Issue: 3, page 426-451
- ISSN: 1292-8119

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topMennucci, Andrea C.G.. "Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I: Regularity." ESAIM: Control, Optimisation and Calculus of Variations 10.3 (2010): 426-451. <http://eudml.org/doc/90737>.

@article{Mennucci2010,

abstract = {
We formulate an Hamilton-Jacobi partial differential equation
H( x, D u(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
“minsol solution” u, a generalized solution;
to this end, we view T*M
as a symplectic manifold.
The definition of “minsol 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
$\{\{\mathcal H\}\}^\{n-1\}$ negligeable subset.
These results can be applied to the cutlocus of a C2 submanifold
of a Finsler manifold.
},

author = {Mennucci, Andrea C.G.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Hamilton-Jacobi equations; conjugate points.; Hamilton-Jacobi equation; manifold; min solution; viscosity solution; geodesics; regularity; conjugate points; Finsler manifold},

language = {eng},

month = {3},

number = {3},

pages = {426-451},

publisher = {EDP Sciences},

title = {Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I: Regularity},

url = {http://eudml.org/doc/90737},

volume = {10},

year = {2010},

}

TY - JOUR

AU - Mennucci, Andrea C.G.

TI - Regularity and variationality of solutions to Hamilton-Jacobi equations. Part I: Regularity

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 10

IS - 3

SP - 426

EP - 451

AB -
We formulate an Hamilton-Jacobi partial differential equation
H( x, D u(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
“minsol solution” u, a generalized solution;
to this end, we view T*M
as a symplectic manifold.
The definition of “minsol 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
${{\mathcal H}}^{n-1}$ negligeable subset.
These results can be applied to the cutlocus of a C2 submanifold
of a Finsler manifold.

LA - eng

KW - Hamilton-Jacobi equations; conjugate points.; Hamilton-Jacobi equation; manifold; min solution; viscosity solution; geodesics; regularity; conjugate points; Finsler manifold

UR - http://eudml.org/doc/90737

ER -

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