On the lack of compactness in the axisymmetric neo-Hookean model
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2021
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914659932569600 |
|---|---|
| author | Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy |
| author_facet | Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_07112 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On the lack of compactness in the axisymmetric neo-Hookean model Barchiesi, Marco Henao, Duvan Mora-Corral, Carlos Rodiac, Rémy Analysis of PDEs 74B20, 49J45, 49Q20, 74G70, 74G65, 74G45, 74G22 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. |
| title | On the lack of compactness in the axisymmetric neo-Hookean model |
| topic | Analysis of PDEs 74B20, 49J45, 49Q20, 74G70, 74G65, 74G45, 74G22 |
| url | https://arxiv.org/abs/2111.07112 |