  In this paper we consider the elastic energy for open curves in Euclidean
space subject to clamped boundary conditions and obtain the \L ojasiewicz-Simon
gradient inequality for this energy functional. Thanks to this inequality we
can prove that a (suitably reparametrized) solution to the associated
$L^2$-gradient flow converges for large time to an elastica, that is to a
critical point of the functional.
