Some minimization problems for planar networks of elastic curves

Anna Dall’Acqua, and Alessandra Pluda. "Some minimization problems for planar networks of elastic curves." Geometric Flows 2.1 (2017): null. <http://eudml.org/doc/288405>.

@article{AnnaDall2017,
abstract = {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).},
author = {Anna Dall’Acqua, Alessandra Pluda},
journal = {Geometric Flows},
keywords = {Elastic energy; networks; Euler-Lagrange equations; fourth order},
language = {eng},
number = {1},
pages = {null},
title = {Some minimization problems for planar networks of elastic curves},
url = {http://eudml.org/doc/288405},
volume = {2},
year = {2017},
}

TY - JOUR
AU - Anna Dall’Acqua
AU - Alessandra Pluda
TI - Some minimization problems for planar networks of elastic curves
JO - Geometric Flows
PY - 2017
VL - 2
IS - 1
SP - null
AB - 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).
LA - eng
KW - Elastic energy; networks; Euler-Lagrange equations; fourth order
UR - http://eudml.org/doc/288405
ER -