2025/04/08 by Marius Müller, Müller, Marius, Kensuke Yoshizawa +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2504.05927
openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study an obstacle problem for the length-penalized elastic bending energy for open planar curves pinned at the boundary. We first consider the case without length penalization and investigate the role of global minimizers among graph curves in our minimization problem for planar curves. In addition, for large values of the length-penalization parameter λ>0, we expose an explicit threshold parameter above which minimizers touch the obstacle, regardless of its shape. On contrary, for small values of λ>0 we show that the minimizers do not touch the obstacle, and they are given by an explicit elastica.