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Let X be a reflexive Banach space and Y its dual. In this paper we findnecessary and sufficient conditions for the existence of a bipotential for ablurred maximal cyclically monotone graph. Equivalently, we find a necessaryand sufficient condition on $\phi \in \Gamma_{0}(X)$ for that the differentialinclusion $y \in \bar{B}(\epsilon) + \partial \phi(x)$ can be put in the form$y \in \partial b(\cdot, y)(x)$, with $b$ a bipotential.

Blurred maximal cyclically monotone sets and bipotentials