We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set . We prove existence, regularity and some structural properties of minimizers. In particular, when is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a minimizer with self-intersections.
Accepté le :
DOI : 10.1051/cocv/2016073
Keywords: Minimization, confined curves, elastic energy, bending energy
Dayrens, François 1 ; Masnou, Simon 1 ; Novaga, Matteo 2
@article{COCV_2018__24_1_25_0,
author = {Dayrens, Fran\c{c}ois and Masnou, Simon and Novaga, Matteo},
title = {Existence, regularity and structure of confined elasticae},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {25--43},
year = {2018},
publisher = {EDP Sciences},
volume = {24},
number = {1},
doi = {10.1051/cocv/2016073},
mrnumber = {3764132},
zbl = {1397.49020},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2016073/}
}
TY - JOUR AU - Dayrens, François AU - Masnou, Simon AU - Novaga, Matteo TI - Existence, regularity and structure of confined elasticae JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 25 EP - 43 VL - 24 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2016073/ DO - 10.1051/cocv/2016073 LA - en ID - COCV_2018__24_1_25_0 ER -
%0 Journal Article %A Dayrens, François %A Masnou, Simon %A Novaga, Matteo %T Existence, regularity and structure of confined elasticae %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 25-43 %V 24 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2016073/ %R 10.1051/cocv/2016073 %G en %F COCV_2018__24_1_25_0
Dayrens, François; Masnou, Simon; Novaga, Matteo. Existence, regularity and structure of confined elasticae. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 25-43. doi: 10.1051/cocv/2016073
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