Some minimization problems for planar networks of elastic curves

• Autorzy: Anna Dall’Acqua , Alessandra Pluda
• Języki publikacji: EN

Abstrakty

EN

In this note we announce some results that will appear in [6] on the minimization of the functional F(Γ) = ∫Γk2 + 1 ds, where Γ is a network of three curves with fixed equal angles at the two junctions. The informal description of the results is accompanied by a partial review of the theory of elasticae and a diffuse discussion about the onset of interesting variants of the original problem passing from curves to networks. The considered energy functional F is given by the elastic energy and a term that penalize the total length of the network.We will show that penalizing the length is tantamount to fix it. The paper is concluded with the explicit computation of the penalized elastic energy of the “Figure Eight”, namely the unique closed elastica with self-intersections (see Figure 1).

Słowa kluczowe

EN

Elastic energy; networks; Euler-Lagrange equations; fourth order

Kategorie tematyczne

• 49J45: Methods involving semicontinuity and convergence; relaxation
• 49-02: Research exposition (monographs, survey articles)
• 53A04: Curves in Euclidean space
• 49J05: Free problems in one independent variable

• Wydawca: De Gruyter Open
• Czasopismo: Geometric Flows
• Rocznik: 2017
• Tom: 2
• Numer: 1

Daty

wydano

2017-12-20

otrzymano

2017-09-15

zaakceptowano

2017-10-27

online

2017-12-29

Twórcy

autor

Anna Dall’Acqua

• ,

autor

Alessandra Pluda

• ,

Identyfikatory

DOI

10.1515/geofl-2017-0005