Lower semicontinuity, Stoilow factorization and principal maps
act. We consider a refinement of the usual quasiconvexity condition of Morrey in two dimensions that allows us to prove lower semicontinuity and existence of minimizers for a class of functionals which are unbounded as the determinant vanishes and are non-polyconvex in general. This notion, that we...
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
American Institute of Mathematical Sciences
2024
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| _version_ | 1811140348235218944 |
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| author | Astala, K Faraco, D Guerra, A Koski, A Kristensen, JAN |
| author_facet | Astala, K Faraco, D Guerra, A Koski, A Kristensen, JAN |
| author_sort | Astala, K |
| collection | OXFORD |
| description | act. We consider a refinement of the usual quasiconvexity condition of
Morrey in two dimensions that allows us to prove lower semicontinuity and
existence of minimizers for a class of functionals which are unbounded as the
determinant vanishes and are non-polyconvex in general. 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. We also describe local conditions which combined with quasiconvexity
yield principal quasiconvexity. The Stoilow factorization, that in the context
of maps of integrable distortion was developed by Iwaniec and Sver´ak, plays a ˇ
prominent role in our app |
| first_indexed | 2024-09-25T04:20:33Z |
| format | Journal article |
| id | oxford-uuid:6ec2c67a-c65e-4466-8375-799b18706f77 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:20:33Z |
| publishDate | 2024 |
| publisher | American Institute of Mathematical Sciences |
| record_format | dspace |
| spelling | oxford-uuid:6ec2c67a-c65e-4466-8375-799b18706f772024-08-02T15:24:23ZLower semicontinuity, Stoilow factorization and principal mapsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6ec2c67a-c65e-4466-8375-799b18706f77EnglishSymplectic ElementsAmerican Institute of Mathematical Sciences2024Astala, KFaraco, DGuerra, AKoski, AKristensen, JANact. We consider a refinement of the usual quasiconvexity condition of Morrey in two dimensions that allows us to prove lower semicontinuity and existence of minimizers for a class of functionals which are unbounded as the determinant vanishes and are non-polyconvex in general. 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. We also describe local conditions which combined with quasiconvexity yield principal quasiconvexity. The Stoilow factorization, that in the context of maps of integrable distortion was developed by Iwaniec and Sver´ak, plays a ˇ prominent role in our app |
| spellingShingle | Astala, K Faraco, D Guerra, A Koski, A Kristensen, JAN Lower semicontinuity, Stoilow factorization and principal maps |
| title | Lower semicontinuity, Stoilow factorization and principal maps |
| title_full | Lower semicontinuity, Stoilow factorization and principal maps |
| title_fullStr | Lower semicontinuity, Stoilow factorization and principal maps |
| title_full_unstemmed | Lower semicontinuity, Stoilow factorization and principal maps |
| title_short | Lower semicontinuity, Stoilow factorization and principal maps |
| title_sort | lower semicontinuity stoilow factorization and principal maps |
| work_keys_str_mv | AT astalak lowersemicontinuitystoilowfactorizationandprincipalmaps AT faracod lowersemicontinuitystoilowfactorizationandprincipalmaps AT guerraa lowersemicontinuitystoilowfactorizationandprincipalmaps AT koskia lowersemicontinuitystoilowfactorizationandprincipalmaps AT kristensenjan lowersemicontinuitystoilowfactorizationandprincipalmaps |