Calculus of Variations and Geometric Measure Theory

M. Barchiesi - D. Henao - C. Mora-Corral - R. Rodiac

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

created by barchiesi on 26 Jan 2024
modified on 26 Feb 2024


Published Paper

Inserted: 26 jan 2024
Last Updated: 26 feb 2024

Journal: Forum of Mathematics, Sigma
Volume: 12
Year: 2024

ArXiv: 2111.07112 PDF
Links: official version


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.

Keywords: relaxation, neo-Hookean, dipole