Inserted: 10 jan 2019
Last Updated: 12 jan 2021
Journal: Comm. Partial Differential Equations
The $L^2$–gradient flow of the elastic energy of networks leads to a Willmore type evolu- tion law with nontrivial nonlinear boundary conditions. We show local in time existence and uniqueness for this elastic flow of networks in a Sobolev space setting under natu- ral boundary conditions. In addition we show a regularisation property and geometric existence and uniqueness. The main result is a long time existence result using energy methods.