L2-flow of elastic curves with clamped boundary conditions

In this paper we investigate the L2-flow of elastic curves with clamped boundary conditions in n-dimensional Euclidean spaces. The L2-flow corresponds to a fourth-order parabolic equation. In the case of closed curves, the long-time existence of solutions of this evolution equation has been derived in the literature. We extend this result to the case of open (i.e., non-closed) curves with clamped boundary conditions.