Submitted Paper

Inserted: 25 mar 2026
Last Updated: 25 mar 2026

Year: 2026

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.

Keywords: nonlinear elasticity, neo-Hookean energy

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• Lavrentiev