On nonconvex subdifferential calculus in Banach spaces.
On strong continuity of derivatives of mappings
On subdifferentials of convex functions
On the differentiability of multivalued mappings. I.
On the differentiability of multivalued mappings. II.
On the geometric characterization of differentiability. I.
On the geometric characterization of differentiability. II.
On the graduated derivatives.
On the Lie algebra of vertical prolongation operators
On the range of the derivative of a smooth function and applications.
We survey recent results on the structure of the range of the derivative of a smooth real valued function f defined on a real Banach space X and of a smooth mapping F between two real Banach spaces X and Y. We recall some necessary conditions and some sufficient conditions on a subset A of L(X,Y) for the existence of a Fréchet-differentiable mapping F from X into Y so that F'(X) = A. Whenever F is only assumed Gâteaux-differentiable, new phenomena appear: we discuss the existence of a mapping F...
On the tangency of multifunctions
Optimality conditions for problems with set-valued objectives.
Relèvement linéaire des cobords
Remarks of germs in infinite dimensions.
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....
Remarks on subdifferentials of convex functionals
Restrictive metric regularity and generalized differential calculus in Banach spaces.
Second order differentiability and Lipschitz smooth points of convex functionals
Singlevaluedness of monotone operators on subspaces of GSG spaces
We extend Zajíček’s theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a -cone supported set.
Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces