Elastic curves and phase transitions
Mathematische Annalen, ISSN: 1432-1807, Vol: 376, Issue: 3-4, Page: 1629-1674
2020
- 14Citations
- 15Captures
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Article Description
This paper is devoted to a classical variational problem for planar elastic curves of clamped endpoints, so-called Euler’s elastica problem. We investigate a straightening limit that means enlarging the distance of the endpoints, and obtain several new results concerning properties of least energy solutions. In particular we reach a first uniqueness result that assumes no symmetry. As a key ingredient we develop a foundational singular perturbation theory for the modified total squared curvature energy. It turns out that our energy has almost the same variational structure as a phase transition energy of Modica–Mortola type at the level of a first order singular limit.
Bibliographic Details
Springer Science and Business Media LLC
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