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arXiv · 1412.4386

Weak subdifferentials, $r_L$-density and maximal monotonicity

Stephen Simons·Xianfu Wang
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Abstract

In this paper, we first investigate an abstract subdifferential for which (using Ekeland's variational principle) we can prove an analog of the Br{\o}ndsted-Rockafellar property. We introduce the "$r_L$-density" of a subset of the product of a Banach space with its dual. A closed $r_L$-dense monotone set is maximally monotone, but we will also consider the case of nonmonotone closed $r_L$-dense sets. As a special case of our results, we can prove Rockafellar's result that the subdifferential of a proper convex lower semicontinuous function is maximally monotone.

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Stephen Simons, Xianfu Wang. 2014-12-14. Weak subdifferentials, $r_L$-density and maximal monotonicity. https://doi.org/10.1007/s11228-015-0326-7

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