Extensions of convex functions with prescribed subdifferentials
Volume 253 / 2020
Studia Mathematica 253 (2020), 199-213
MSC: 26B05, 26B25, 49J52, 54C20, 54C60.
DOI: 10.4064/sm181212-17-5
Published online: 21 January 2020
Abstract
Let be an arbitrary subset of a Banach space X, f: E \rightarrow \mathbb {R} a function, and G:E \rightrightarrows X^* a set-valued mapping. We give necessary and sufficient conditions on f, G for the existence of a continuous convex extension F: X \rightarrow \mathbb {R} of f such that the subdifferential \partial F of F coincides with G on E.
