Stability and convergence for the length-penalized elastic flow of curves with partial free boundary
Antonia Diana · arXiv (Cornell University) · 2025
We investigate the asymptotic stability of the length-penalized elastic flow of curves with boundary points constrained to the $x$-axis in $\mathbb{R}^2$. The main tool in our analysis is the Lojasiewicz--Simon inequality, which is used to prove that the flow smoothly converges to an elastica.