Short time existence for the elastic flow of clamped curves

Abstract

Abstract We show well‐posedness of the elastic flow of open curves with clamped boundary conditions. To show short time existence we prove that the linearised problem has the property of maximal ‐regularity and use the contraction principle to obtain the solution. Moreover, we show analyticity of the solution and its analytic dependency on the initial curve. With the developed methods we also prove long time existence of the flow if the initial curve is close to an elastica.