Geodesic
Existence, regularity and structure of confined elasticae
Dayrens, François 1 idref     ; Masnou, Simon 1 idref     ; Novaga, Matteo 2 idref   orcid  
1 Institut Camille Jordan, Université Lyon 1, 43, Boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France.
2 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 1, pp. 25-43 Cet article a éte moissonné depuis la source Numdam

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We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set Ω. We prove existence, regularity and some structural properties of minimizers. In particular, when Ω is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a minimizer with self-intersections.

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DOI : 10.1051/cocv/2016073
Classification : 49J52, 49N60, 49Q10, 53A04
Keywords: Minimization, confined curves, elastic energy, bending energy

Dayrens, François  1   ; Masnou, Simon  1   ; Novaga, Matteo  2

1 Institut Camille Jordan, Université Lyon 1, 43, Boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France.
2 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy. 
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     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 = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016073/}
}
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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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