  The most important open problem in Monotone Operator Theory concerns the
maximal monotonicity of the sum of two maximally monotone operators provided
that the classical Rockafellar's constraint qualification holds, which is
called the "sum problem".
  In this paper, we establish the maximal monotonicity of $A+B$ provided that
$A$ and $B$ are maximally monotone operators such that $\dom A\cap\inte\dom
B\neq\varnothing$, and $A+N_{\overline{\dom A}}$ is of type (FPV). This
generalizes various current results and also gives an affirmative answer to a
problem posed by Borwein and Yao. Moreover, we present an equivalent
description of the sum problem.
