  With aim of finding mathematical criteria for contact line depinning from
sharp corners, we have studied the equilibrium and stability of a semi-infinite
planar liquid layer pinned at the vertex of a wedge. Equilibrium is compatible
with a fan of apparent contact angles $\theta_0$ bracketed by the equilibrium
contact angles of both flanks of the wedge, so the contact line could remain
pinned if $\theta_0$ is within this fan. However, the analysis of the stability
of these solutions, studied exploiting the variational structure of the problem
through turning-point arguments, shows that the equilibrium becomes unstable at
critical depinning advancing $\theta_0^a$ and receding $\theta_0^r$ contact
angles, which are found as subcritical saddle-node bifurcations. Equilibrium is
thus possible (stable) within the interval $\theta_0^a < \theta_0 <\theta_0^a$
but the contact line depins from the vertex beyond these critical angles if
they occur within the equilibrium fan.
