Lebesgue measure and mappings of the Sobolev class
We present a survey of the Lusin condition (N) for -Sobolev mappings defined in a domain G of . Applications to the boundary behavior of conformal mappings are discussed.
Lemme div-curl et renormalisation
Les effets de l’exposant de la fonction barrière multiplicative dans les méthodes de points intérieurs
Les méthodes de points intérieurs en programmation linéaire connaissent un grand succès depuis l’introduction de l’algorithme de Karmarkar. La convergence de l’algorithme repose sur une fonction potentielle qui, sous sa forme multiplicative, fait apparaître un exposant . Cet exposant est, de façon générale, choisi supérieur au nombre de variables du problème. Nous montrons dans cet article que l’on peut utiliser des valeurs de plus petites que . Ceci permet d’améliorer le conditionnement de...
Les effets de l'exposant de la fonction barrière multiplicative dans les méthodes de points intérieurs
Les méthodes de points intérieurs en programmation linéaire connaissent un grand succès depuis l'introduction de l'algorithme de Karmarkar. La convergence de l'algorithme repose sur une fonction potentielle qui, sous sa forme multiplicative, fait apparaître un exposant p. Cet exposant est, de façon générale, choisi supérieur au nombre de variables n du problème. Nous montrons dans cet article que l'on peut utiliser des valeurs de p plus petites que n. Ceci permet d'améliorer le conditionnement...
L’espace linéaire des fonctions cliquées sur est généré par les fonctions quasi-continues
Level sets of continuous functions increasing with respect to each variable
We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation φ∘f = gφ + h (cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.
Limit behaviour of trajectories involving subgradients of convex functions
Linear bilipschitz extension property.
Linear functional inequalities-a general theory and new special cases [Book]
Lineare zweidimensionale Räume von stetigen Funktionen mit stetigen ersten Ableitungen
Liouville type theorems for mappings with bounded (co)-distortion
We obtain Liouville type theorems for mappings with bounded -distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded -codistorsion.
Lipschitz and bi-Lipschitz functions.
Lipschitz classes and Poisson integrals on stratified groups
Lipschitz functions with unexpectedly large sets of nondifferentiability points.
Lipschitz mappings, contingents, and differentiability.
Lipschitz r-continuity of the approximative subdifferential of a convex function.
Lipschitz sums of convex functions
We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of Δ-convex functions.
Local solvability of a constrained gradient system of total variation.
Logarithmically concave functions and sections of convex sets in
Lower semicontinuity of multiple -quasiconvex integrals
Lower semicontinuity results are obtained for multiple integrals of the kind , where is a given positive measure on , and the vector-valued function belongs to the Sobolev space associated with . The proofs are essentially based on blow-up techniques, and a significant role is played therein by the concepts of tangent space and of tangent measures to . More precisely, for fully general , a notion of quasiconvexity for along the tangent bundle to , turns out to be necessary for lower...