Calculus of Variations and Geometric Measure Theory
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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 28 Jan 2019

[BibTeX]

Preprint

Inserted: 10 jan 2019
Last Updated: 28 jan 2019

Year: 2019

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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