Geodesic
Integrability of Pseudomonotone Differentiable Maps and the Revealed Preference Problem
Journal of convex analysis, Tome 12 (2005) no. 2, pp. 431-446.

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

\newcommand{\R}{{\mathbb R}} \newcommand{\norm}{\vert\vert} The problem considered is as follows: given $C\subset \R^n$ and $F:C\rightarrow \R^n$ differentiable, find $f:C\rightarrow \R$ differentiable such that $\norm \nabla f(x)\norm^{-1} \nabla f(x) = \norm F(x) \norm^{-1}F(x)$ for all $x\in C$. Conditions for $f$ to be pseudoconvex or convex are given. The results are applied to the differentiable case of the revealed preference problem.
Classification : 90A40, 90C26, 52A41, 47N10, 47H05
Mots-clés : Generalized convexity, generalized monotonicity, consumer theory, direct and indirect utility functions, revealed preference theory 
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     author = {J.-P. Crouzeix and T. Rapcs\'ak},
     title = {Integrability of {Pseudomonotone} {Differentiable} {Maps} and the {Revealed} {Preference} {Problem}},
     journal = {Journal of convex analysis},
     pages = {431--446},
     publisher = {mathdoc},
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     number = {2},
     year = {2005},
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J.-P. Crouzeix; T. Rapcsák. Integrability of Pseudomonotone Differentiable Maps and the Revealed Preference Problem. Journal of convex analysis, Tome 12 (2005) no. 2, pp. 431-446. http://geodesic.mathdoc.fr/item/JCA_2005_12_2_JCA_2005_12_2_a12/