The paper deals with the calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various conditions for calmness, which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmooth analysis. In particular, we focus on nonsmooth calculus and solution stability in mathematical pro...

In this paper we deal with the regularity of planar optimal transport maps, in a “critical” case not covered presently in the literature. Following a suggestion by J.Maly, and the ideas in [1], we relate the regularity problem to a “rigidity” problem for partial differential inclusions which might be interesting in its own right. Let us start with the first problem. We give a formulation in ter...

Continuing the work of Hiriart-Urruty and Phelps, we discuss (in both locally convex spaces and Banach spaces) the formulas for the conjugates and subdifferentials of the precomposition of a convex function by a continuous linear mapping and the marginal function of a convex function by a continuous linear mapping. We exhibit a certain (incomplete) duality between the operations of precompositi...