Lower semicontinuity, Stoilow factorization and principal maps
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915494448070656 |
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| author | Astala, Kari Faraco, Daniel Guerra, André Koski, Aleksis Kristensen, Jan |
| author_facet | Astala, Kari Faraco, Daniel Guerra, André Koski, Aleksis Kristensen, Jan |
| contents | We consider a strengthening of the usual quasiconvexity condition of Morrey in two dimensions, which allows us to prove lower semicontinuity for functionals which are unbounded as the determinant vanishes. This notion, that we call principal quasiconvexity, arose from the planar theory of quasiconformal mappings and mappings of finite distortion. We compare it with other quasiconvexity conditions that have appeared in the literature and provide a number of concrete examples of principally quasiconvex functionals that are not polyconvex. The Stoilow factorization, that in the context of maps of integrable distortion was developed by Iwaniec and Šverák, plays a prominent role in our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lower semicontinuity, Stoilow factorization and principal maps Astala, Kari Faraco, Daniel Guerra, André Koski, Aleksis Kristensen, Jan Analysis of PDEs Complex Variables We consider a strengthening of the usual quasiconvexity condition of Morrey in two dimensions, which allows us to prove lower semicontinuity for functionals which are unbounded as the determinant vanishes. This notion, that we call principal quasiconvexity, arose from the planar theory of quasiconformal mappings and mappings of finite distortion. We compare it with other quasiconvexity conditions that have appeared in the literature and provide a number of concrete examples of principally quasiconvex functionals that are not polyconvex. The Stoilow factorization, that in the context of maps of integrable distortion was developed by Iwaniec and Šverák, plays a prominent role in our approach. |
| title | Lower semicontinuity, Stoilow factorization and principal maps |
| topic | Analysis of PDEs Complex Variables |
| url | https://arxiv.org/abs/2401.16138 |