The most important open problem in Monotone Operator Theory concerns the
maximal monotonicity of the sum of two maximal monotone operators provided that
Rockafellar's constraint qualification holds. In this paper, we provide a new
maximal monotonicity result for the sum of two maximal monotone operators $A$
and $B$ in this setting satisfying that $A+N_{\bar{\dom B}}$ is of type (FPV)
and $\dom A\cap\bar{\dom B}\subseteq\dom B$. The proof relies on some results
on the Fitzpatrick function.