Bounded variation and differentiability of functions.
BV-sets, functions and integrals
extensions of functions and stabilization of Glaeser refinements.
-minimal pairs of compact convex sets.
C1,... partial regularity of functions minimising quasiconvex integrals.
Caractère lipschitzien d'une distance associée à des champs de vecteurs engendrant une algèbre de Lie de rang maximal. Quelques conséquences
La métrique attachée de façon naturelle à des champs de vecteurs est susceptible de plusieurs définitions voisines ; on montre que, suivant la définition adoptée, elle peut avoir, ou ne pas avoir, un caractère localement lipschitzien qui a pour conséquence l’existence de points -réguliers, pour certains opérateurs différentiels , sur les frontières des boules pour la métrique.
Change of variables formula under minimal assumptions
In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We only need...
Characterization of convex functions
There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite-Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.
Characterizations of convex vector functions and optimization.
Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings.
Companion inequalities to Jensen's inequality for -convex and -convex functions.
Compensated convexity and its applications
Complément de Schur et sous-différentiel du second ordre d'une fonction convexe.
Complements, approximations, smoothings and invariance properties.
Complete extension of a convex function
Complex interpolation of function spaces with general weights
We present the complex interpolation of Besov and Triebel–Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel–Lizorkin spaces. As a corollary of our results, we obtain the complex interpolation between the weighted Triebel–Lizorkin spaces and with suitable assumptions on the parameters and , and the pair of weights .
Complexity of the class of Peano functions
We evaluate the descriptive set theoretic complexity of the space of continuous surjections from to .
Computation of Lojasiewicz Exponent of ...(x, y)
Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût
Concerning the existence of the double Stieltjes mean -integral