Variational representations for N-cyclically monotone vector fields

Alfred Galichon, Nassif Ghoussoub

Given a convex bounded domain $\Omega$ in ${\mathbb{R}}^d$ and an integer $N\ge 2$, we associate to any jointly $N$-monotone $(N-1)$-tuplet $(u_1,u_2,...,u_{N-1})$ of vector fields…