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arXiv · 2111.07112

On the lack of compactness in the axisymmetric neo-Hookean model

Marco Barchiesi·Duvan Henao·Carlos Mora-Corral·Rémy Rodiac
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Abstract

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-- 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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Marco Barchiesi, Duvan Henao, Carlos Mora-Corral, Rémy Rodiac. 2021-11-13. On the lack of compactness in the axisymmetric neo-Hookean model. https://arxiv.org/abs/2111.07112

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