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• W3214418506 abstract "In this paper we pursue the study, started in arXiv:2102.12303, of the relaxation of the neo-Hookean energy defined originally in an axisymmetric setting and in a functional space where no cavitation is allowed. We provide a matching upper bound for the lower bound on the relaxation functional derived in our previous paper in the particular case of a singular map described by Conti-De Lellis and corresponding to a dipole. This is a supplementary justification to study the regularity of the modified neo-Hookean functional we proposed in our previous paper. We also give a finer description of weak limits of regular maps under the assumption that they have finite surface energy. In this case we prove that these weak limits have a dipole structure showing that the Conti-De Lellis map is generic in some sense. In the last part of the paper we make a link with Cartesian currents showing that the lower bound on the relaxation we obtained presents strong similarities with the relaxed energy in the context of $mathbb{S}^2$-valued harmonic maps." @default.
• W3214418506 created "2021-11-22" @default.
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• W3214418506 date "2021-11-13" @default.
• W3214418506 modified "2023-09-27" @default.
• W3214418506 title "On the lack of compactness problem in the axisymmetric neo-Hookean model" @default.
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