  We consider the standard first passage percolation model in the rescaled
lattice $\mathbb Z^d/n$ for $d\geq 2$ and a bounded domain $\Omega$ in $\mathbb
R^d$. We denote by $\Gamma^1$ and $\Gamma^2$ two disjoint subsets of $\partial
\Omega$ representing respectively the sources and the sinks, \textit{i.e.},
where the water can enter in $\Omega$ and escape from $\Omega$. A cutset is a
set of edges that separates $\Gamma ^1$ from $\Gamma^2$ in $\Omega$, it has a
capacity given by the sum of the capacities of its edges. Under some
assumptions on $\Omega$ and the distribution of the capacities of the edges, we
already know a law of large numbers for the sequence of minimal cutsets
$(\mathcal E_n^{min})_{n\geq 1}$: the sequence $(\mathcal E_n^{min})_{n\geq 1}$
converges almost surely to the set of solutions of a continuous deterministic
problem of minimal cutset in an anisotropic network. We aim here to derive a
large deviation principle for cutsets and deduce by contraction principle a
lower large deviation principle for the maximal flow in $\Omega$.
