Maximal monotone operators are selfdual vector fields and vice-versa

Nassif Ghoussoub

If $L$ is a selfdual Lagrangian $L$ on a reflexive phase space $X\times X^{\ast }$, then the vector field $x\to \bar{\partial }L(x):=\{p\in X^{\ast };(p,x)\in \partial L(x,p)\}$ is maximal mono…