Classification and stability of penalized pinned elasticae
- This paper considers critical points of the length-penalized elastic bending energy among planar curves whose endpoints are fixed. We classify all critical points with an explicit parametrization. The classification strongly depends on a special penalization parameter λˆ ≃ 0.70107. Stability of all the critical points is also investigated, and again the threshold λˆ plays a decisive role. In addition, our explicit parametrization is applied to compare the energy of critical points, leading to uniqueness of minimal nontrivial critical points. As an application we obtain eventual embeddedness of elastic flows.
| Author: | Marius MüllerGND, Kensuke Yoshizawa |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1268538 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/126853 |
| ISSN: | 0022-0396OPAC |
| Parent Title (English): | Journal of Differential Equations |
| Publisher: | Elsevier BV |
| Place of publication: | Amsterdam |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2026 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/12/08 |
| Volume: | 454 |
| First Page: | 113941 |
| DOI: | https://doi.org/10.1016/j.jde.2025.113941 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
