Decrease of C1,1 property in vector optimization
In the paper we generalize sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Rocca, and by authors with the help of the notion of ℓ-stability for vector functions.
Derivatives of Hadamard type in scalar constrained optimization
Vsevolod I. Ivanov stated (Nonlinear Analysis 125 (2015), 270-289) the general second-order optimality condition for the constrained vector problem in terms of Hadamard derivatives. We will consider its special case for a scalar problem and show some corollaries for example for -stable at feasible point functions. Then we show the advantages of obtained results with respect to the previously obtained results.
Description du défaut de compacité de l'injection de Sobolev
Description of the lack of compactness for the Sobolev imbedding
We prove that any bounded sequence in a Hilbert homogeneous Sobolev space has a subsequence which can be decomposed as an almost-orthogonal sum of a sequence going strongly to zero in the corresponding Lebesgue space, and of a superposition of terms obtained from fixed profiles by applying sequences of translations and dilations. This decomposition contains in particular the various versions of the concentration-compactness principle.
Développements analytiques, pour servir à compléter la discussion de la variation seconde des intégrales définies multiples
Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations
Duality and best constant for a Trudinger–Moser inequality involving probability measures