Published Paper

Inserted: 9 oct 2023
Last Updated: 28 aug 2024

Journal: Partial Differential Equations and Applications
Volume: 5
Number: Paper n. 28
Year: 2024
Doi: 10.1007/s42985-024-00300-3

Abstract:

In this article we study the anisotropic curve shortening flow for a planar network of three curves with fixed endpoints and which meet in a triple junction. We show that the anisotropic curvature energy fulfills a Lojasiewicz-Simon gradient inequality and use this knowledge to derive stability results for the flow. Precisely, in our main theorem we show that for any initial data, which are $C^{2+\alpha}$-close to a (local) energy minimizer, the flow exists globally and converges to a possibly different energy minimum.