Calculus of Variations and Geometric Measure Theory

H. Garcke - J. Menzel - A. Pluda

Long Time Existence of Solutions to an Elastic Flow of Networks

created by pluda on 10 Jan 2019
modified on 12 Jan 2021


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


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.