A New Proof of the Maximal Monotonicity of Subdifferentials

We give a new proof based on the recent very elegant argument of M. Marques Alves and B. F. Svaiter [J. Convex Analysis 15 (2008) 345--348] that the subdifferential of a proper, convex lower semicontinuous function on a real Banach space is maximally monotone. We also show how the argument can be simplified in the reflexive case