Submonotone Subdifferentials of Lipschitz Functions

^-representation of Subdifferentials of Directionally Lipschitz Functions

Subdifferentials of convex functions and some regular functions f are expressed in terms of limiting gradients at points in a given dense subset of dorn Vf.

Integrability of Subdifferentials of Directionally Lipschitz Functions

Using a quantitative version of the subdifferential characterization of directionally Lipschitz functions, we study the integrability of subdifferentials of such functions over arbitrary Banach space.

Rotund Norms, Clarke Subdifferentials and Extensions of Lipschitz Functions

Lipschitz functions with maximal Clarke subdifferentials are staunch

In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire’s category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only of generic, but also staunch. 1991 Mathematics Subject Classification: Primary 49J52.

Characterization of the Subdifferentials of Convex Functions

Each lower semi-continuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E* called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones whose graphs are maximal "cyclically monotone" relations on Ex E*, and that each of these is also a maximal monotone relation. Furthermore, it is proved that of de...