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

Abstract

AbstractWe prove short-time existence for the negative$$L^2$$L2-gradient flow of thep-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$$W^{2,p}$$W2,p-Sobolev norm of the initial data.