A Lavrentiev phenomenon in the neo-Hookean model
Analysis of PDEs
2026-03-25 v1
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 -closure of that class. The mechanism underlying the gap is a deformation with a dipole-type singularity.
Cite
@article{arxiv.2603.22873,
title = {A Lavrentiev phenomenon in the neo-Hookean model},
author = {Marco Barchiesi and Duvan Henao and Carlos Mora-Corral and Rémy Rodiac},
journal= {arXiv preprint arXiv:2603.22873},
year = {2026}
}
Comments
25 pages, 5 figures