  The most famous open problem in Monotone Operator Theory concerns the maximal
monotonicity of the sum of two maximally monotone operators provided that
Rockafellar's constraint qualification holds.
  In this paper, we prove the maximal monotonicity of $A+B$ provided that $A,
B$ are maximally monotone and $A$ is a linear relation, as soon as
Rockafellar's constraint qualification holds: $\dom A\cap\inte\dom
B\neq\varnothing$. Moreover, $A+B$ is of type (FPV).
