On the range of the derivative of a smooth function and applications.

Título inglés	On the range of the derivative of a smooth function and applications.
Título español	Estructura del rango de la derivada de una función.
Autor/es	Deville, Robert
Organización	Inst. Math. Univ. Bordeaux I, Talence, Francia
Revista	1578-7303
Publicación	2006, 100 (1-2): 63-74, 21 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We survey recent results on the structure of the range of the derivative of a smooth real valued function f defined on a real Banach space X and of a smooth mapping F between two real Banach spaces X and Y. We recall some necessary conditions and some sufficient conditions on a subset A of L(X,Y) for the existence of a Fréchet-differentiable mapping F from X into Y so that F'(X) = A. Whenever F is only assumed Gâteaux-differentiable, new phenomena appear: we discuss the existence of a mapping F from a Banach space X into a Banach space Y, which is bounded, Lipschitz-continuous, and so that for all x, y Î X, if x ≠ y, then ||F'(x) - F'(y)||L(X,Y) > 1. Applications are given to existence and uniqueness of solutions of Hamilton-Jacobi equations.
Código MathReviews	MR2267401
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