  We establish the existence of global weak solutions of the 2D incompressible
Euler equation, for a large class of non-smooth open sets. These open sets are
the complements (in a simply connected domain) of a finite number of connected
compact sets with positive capacity. Existence of weak solutions with $L^p$
vorticity is deduced from an approximation argument, that relates to the
so-called $\Gamma$-convergence of domains. Our results complete those obtained
for convex domains, or for domains with asymptotically small holes. Connection
is made to the recent papers of the second author on the Euler equation in the
exterior of a Jordan arc.
