Geodesic
Geometric Conditions for Regularity in a Time-Minimum Problem with Constant Dynamics
Journal of convex analysis, Tome 19 (2012) no. 3, pp. 631-669.

Voir la notice de l'article provenant de la source Heldermann Verlag

Continuing earlier research [``Neighbourhood retractions of nonconvex sets in a Hilbert space via sublinear functionals'', J. Convex Analysis 18 (2011) 1--36] on local well-posedness of a time-minimum problem associated to a closed target set $C\subset H$ ($H$ is a Hilbert space) and a convex constant dynamics $F\subset H$ we study the Lipschitz (or, in general, H\"{o}lder) regularity of the (unique) point $\pi_{C}^{F}\left( x\right)$ in $C$ achieved from $x$ for a minimal time. As a consequence, smoothness of the value function is proved, and an explicit formula for its derivative is given.
Classification : 49J52, 49N15
Mots-clés : Time-minimum problem, Hoelder continuity, proximal, Frechet subdifferential, Clarke subdifferential, duality mapping, curvature, proximal smoothness 
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     author = {V. V. Goncharov and F. F. Pereira},
     title = {Geometric {Conditions} for {Regularity} in a {Time-Minimum} {Problem} with {Constant} {Dynamics}},
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     pages = {631--669},
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     number = {3},
     year = {2012},
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V. V. Goncharov; F. F. Pereira. Geometric Conditions for Regularity in a Time-Minimum Problem with Constant Dynamics. Journal of convex analysis, Tome 19 (2012) no. 3, pp. 631-669. http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a2/