Blurred maximal cyclically monotone sets and bipotentials

Abstract

Let X be a reflexive Banach space and Y its dual. In this paper we find necessary and sufficient conditions for the existence of a bipotential for a blurred maximal cyclically monotone graph. Equivalently, we find a necessary and sufficient condition on $\varphi \in {\Gamma }_0(X)$ for that the differential inclusion $y\in \bar{B}(\epsilon )+\partial \varphi (x)$ can be put in the form $y\in \partial b(\cdot ,y)(x)$, with $b$ a bipotential.

Revised version, corrections in theorem 6.2

References in corpus (1)

• Bipotentials for non monotone multivalued operators: fundamental results and applications

Cited by in corpus (1)

• Existence results for variational-hemivariational inequality systems with nonlinear couplings