A Lavrentiev phenomenon in the neo-Hookean model
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911541117321216 |
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| author | Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy |
| author_facet | Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22873 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Lavrentiev phenomenon in the neo-Hookean model Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy Analysis of PDEs 49J45, 49S05, 74B20, 74G65 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. |
| title | A Lavrentiev phenomenon in the neo-Hookean model |
| topic | Analysis of PDEs 49J45, 49S05, 74B20, 74G65 |
| url | https://arxiv.org/abs/2603.22873 |