A bifurcation problem involving elastica

Gabutti, Bruno; Lepora, P.; Merlo, Gabriele

doi:10.1007/bf02128926

Cited by 4 publications

(2 citation statements)

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“…To the author's knowledge, there is no general result to determine typical points as (a) or (b) rigorously (cf. [3,34,76]).…”

Section: Introductionmentioning

confidence: 99%

“…For open curves, the stability of post-buckling elasticae is even now a central issue (see e.g. [34,40,59,74,77] and references therein). More recently, basic properties of elastic networks are investigated [24,23]: Along the way it is confirmed in [24] that a global minimizer in a "drop" setting (l = 0 and θ 0 , θ 1 not fixed) is the half figure-eight and thus unique up to rotation.…”

Section: Introductionmentioning

confidence: 99%

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Elastic curves and phase transitions

Miura

2017

Preprint

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This paper is devoted to classical variational problems 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.2010 Mathematics Subject Classification. 49Q10, and 53A04.

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“…To the author's knowledge, there is no general result to determine typical points as (a) or (b) rigorously (cf. [3,34,76]).…”

Section: Introductionmentioning

confidence: 99%