Geodesic
On the lack of compactness in the axisymmetric neo-Hookean model
Forum of Mathematics, Sigma, Tome 12 (2024)

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We provide a fine description of the weak limit of sequences of regular axisymmetric maps with equibounded neo-Hookean energy, under the assumption that they have finite surface energy. We prove that these weak limits have a dipole structure, showing that the singular map described by Conti and De Lellis is generic in some sense. On this map, we provide the explicit relaxation of the neo-Hookean energy. We also make a link with Cartesian currents showing that the candidate for the relaxation we obtained presents strong similarities with the relaxed energy in the context of $\mathbb {S}^2$-valued harmonic maps. 
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     author = {Marco Barchiesi and Duvan Henao and Carlos Mora-Corral and R\'emy Rodiac},
     title = {On the lack of compactness in the axisymmetric {neo-Hookean} model},
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Marco Barchiesi; Duvan Henao; Carlos Mora-Corral; Rémy Rodiac. On the lack of compactness in the axisymmetric neo-Hookean model. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.9

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