Published Paper
Inserted: 10 jan 2019
Last Updated: 12 jan 2021
Journal: Comm. Partial Differential Equations
Volume: 45
Number: 10
Pages: 1253-1305
Year: 2020
Doi: 10.1080/03605302.2020.1771364
Abstract:
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.
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