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arXiv · 2603.22873

A Lavrentiev phenomenon in the neo-Hookean model

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

We exhibit a Lavrentiev gap phenomenon for the neo-Hookean energy in three-dimensional nonlinear elasticity. More precisely, we construct boundary data for which the infimum of the neo-Hookean energy over deformations satisfying a natural regularity and invertibility condition is strictly larger than the infimum over the weak $H^1$-closure of that class. The mechanism underlying the gap is a deformation with a dipole-type singularity.

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Marco Barchiesi, Duvan Henao, Carlos Mora-Corral, Rémy Rodiac. 2026-03-24. A Lavrentiev phenomenon in the neo-Hookean model. https://arxiv.org/abs/2603.22873

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