  In this note, we study maximal monotonicity of linear relations (set-valued
operators with linear graphs) on reflexive Banach spaces. We provide a new and
simpler proof of a result due to Brezis-Browder which states that a monotone
linear relation with closed graph is maximal monotone if and only if its
adjoint is monotone. We also study Fitzpatrick functions and give an explicit
formula for Fitzpatrick functions of order n for monotone symmetric linear
relations.
