E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
-
Published in:
19th Panhellenic Conference on Mathematical Analysis
-
Date (published):
19-Dec-2025
-
Event name:
19th Panhellenic Conference on Mathematical Analysis
en
Event date:
18-Dec-2025 - 20-Dec-2025
-
Event place:
Athen, Greece
-
Number of Pages:
1
-
Keywords:
semicontinuous functions; subdiferential operator; convex function
en
Abstract:
For a monotone operator A : X ⇒ X∗, we define FA as the family of all representations of A through convex lower semicontinuous functions on X×X∗. In this talk we shall discuss the singular case, that is, the family collapses to a singleton. We show that every such operator is cyclically monotone (hence, A = ∂f for some convex function f) if and only if it is 3-monotone. In Radon–Nikod´ym spaces, under mild conditions (which become superfluous in finite dimensions), we prove that a subdifferential operator A = ∂f is uniquely representable if and only if f is the sum of a support and an indicator function of suitable convex sets. This is joint work with Aris Daniilidis.
en
Project title:
Unilateralität und Asymmetrie in der Variationsanalyse: P 36344N (FWF - Österr. Wissenschaftsfonds)
