Minimal elastic networks
Analysis of PDEs
2021-08-25 v2 Differential Geometry
Abstract
We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some properties of the minimal configurations.
Cite
@article{arxiv.1712.09589,
title = {Minimal elastic networks},
author = {Anna Dall'Acqua and Matteo Novaga and Alessandra Pluda},
journal= {arXiv preprint arXiv:1712.09589},
year = {2021}
}
Comments
21 pages, Thanks to a fruitful discussion with Tatsuya Miura the proof of Proposition 4.8 in the current version of the manuscript is more detailed than the one contained in the published version of this paper