Locally efficient monotone operators

Verona, Andrei; Verona, Maria Elena

doi:10.1090/S0002-9939-1990-1012939-0

Locally efficient monotone operators
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by Andrei Verona and Maria Elena Verona PDF

Proc. Amer. Math. Soc. 109 (1990), 195-204 Request permission

Abstract:

We study monotone operators on quasi open or convex subsets of a real Banach space $X$ (quasi open means that the contingent cone at each point equals $X$). Among others we characterize the maximality of such an operator in terms of its ${w^*}$-upper semicontinuity properties and, in the case of a convex domain, also in terms of its behavior at the support points. We next give sufficient conditions for such an operator to be generically single valued, extending Kenderov’s theorems. As an application we reobtain generic Gâteaux and Fréchet differentiability results for convex functions defined on not necessarily open convex sets.

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