The Łojasiewicz-Simon gradient inequality for open elastic curves (Q285657)

The paper deals with the long-time existence of motion of open curves by the gradient flow for the elastic energy. Specifically, the authors show that, given an initial smooth curve, the whole elastic flow of open curves subject to a constraint on the growth of the length converges to a stationary solution. An important step in the proof is to show that the elastic energy functional satisfies the Lojasiewicz-Simon inequality near a critical point.