  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 $\phi \in \Gamma_{0}(X)$ for that the differential
inclusion $y \in \bar{B}(\epsilon) + \partial \phi(x)$ can be put in the form
$y \in \partial b(\cdot, y)(x)$, with $b$ a bipotential.
