On the p-drop theorem, 1 ≤ p ≤∞.
On the points of non-differentiability of convex functions
We characterize sets of non-differentiability points of convex functions on . This completes (in ) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.
On Uniform Differentiability
We introduce the notion of uniform Fréchet differentiability of mappings between Banach spaces, and we give some sufficient conditions for this property to hold.
On σ-porous and Φ-angle-small sets in metric spaces
One counterexample concerning the Fréchet differentiability of convex functions on closed sets
Paraconvex analysis
Proto-differentiability of set-valued mappings and its applications in optimization
Quasi-convex functions and quasi-monotone operators.
Remarks on delta-convex functions
Remarks on Fréchet differentiability of pointwise Lipschitz, cone-monotone and quasiconvex functions
We present some consequences of a deep result of J. Lindenstrauss and D. Preiss on -almost everywhere Fréchet differentiability of Lipschitz functions on (and similar Banach spaces). For example, in these spaces, every continuous real function is Fréchet differentiable at -almost every at which it is Gâteaux differentiable. Another interesting consequences say that both cone-monotone functions and continuous quasiconvex functions on these spaces are -almost everywhere Fréchet differentiable....
Second order differentiability of integral functionals on Sobolev spaces and L2-spaces.
Shape differentiability of the Neumann problem of the Laplace equation in the half-space
Some remarks about strictly pseudoconvex functions with respect to the Clarke-Rockafellar subdifferential.
Some remarks on nonlinear functionals
Sub differentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss
Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings
The paper contains calculus rules for coderivatives of compositions, sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentials in Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials in Asplund spaces and approximate subdifferentials in arbitrary Banach spaces. The key element of the unified approach to obtaining various calculus rules for various types of derivatives presented...
Sufficient conditions for elliptic problem of optimal control in .
Sur les fonctions de lignes fermées
The metric regularity of polynomial functions in one or several variables.