A minimising movement scheme for the p -elastic energy of curves.

We prove short-time existence for the negative L 2 -gradient flow of the p -elastic energy of curves via a minimising movement scheme. In order to account for the degeneracy caused by the energy's invariance under curve reparametrisations, we write the evolving curves as approximate normal graphs over a fixed smooth curve. This enables us to establish short-time existence and give a lower bound on the solution's lifetime that depends only on the W 2 , p -Sobolev norm of the initial data.