On coercive variational integrals
<p>It is well-known that sequential weak lower semicontinuity of a variational integral</p> <p>𝕱(u, Ω) = ∫Ω F (∇u(x)) dx</p> <p>on the Sobolev space W^1,p (Ω, ℝ^N) under a p-growth condition on the integrand F is equivalent to quasiconvexity in the sense of Morrey. We s...
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| Format: | Journal article |
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Elsevier
2016
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| _version_ | 1797105788875964416 |
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| author | Kristensen, J Chen, C |
| author_facet | Kristensen, J Chen, C |
| author_sort | Kristensen, J |
| collection | OXFORD |
| description | <p>It is well-known that sequential weak lower semicontinuity of a variational integral</p> <p>𝕱(u, Ω) = ∫Ω F (∇u(x)) dx</p> <p>on the Sobolev space W^1,p (Ω, ℝ^N) under a p-growth condition on the integrand F is equivalent to quasiconvexity in the sense of Morrey. We show that coercivity on Dirichlet classes likewise is equivalent to a quasiconvexity condition. We also discuss more general notions of coercivity, and in the case of positively p-homogeneous integrands F we establish the existence of minimizers for a class of non-coercive quasiconvex variational integrals.</p> |
| first_indexed | 2024-03-07T06:52:23Z |
| format | Journal article |
| id | oxford-uuid:fcfa67ba-95bd-46fa-9341-ea623611420b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:52:23Z |
| publishDate | 2016 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:fcfa67ba-95bd-46fa-9341-ea623611420b2022-03-27T13:25:14ZOn coercive variational integralsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fcfa67ba-95bd-46fa-9341-ea623611420bSymplectic Elements at OxfordElsevier2016Kristensen, JChen, C<p>It is well-known that sequential weak lower semicontinuity of a variational integral</p> <p>𝕱(u, Ω) = ∫Ω F (∇u(x)) dx</p> <p>on the Sobolev space W^1,p (Ω, ℝ^N) under a p-growth condition on the integrand F is equivalent to quasiconvexity in the sense of Morrey. We show that coercivity on Dirichlet classes likewise is equivalent to a quasiconvexity condition. We also discuss more general notions of coercivity, and in the case of positively p-homogeneous integrands F we establish the existence of minimizers for a class of non-coercive quasiconvex variational integrals.</p> |
| spellingShingle | Kristensen, J Chen, C On coercive variational integrals |
| title | On coercive variational integrals |
| title_full | On coercive variational integrals |
| title_fullStr | On coercive variational integrals |
| title_full_unstemmed | On coercive variational integrals |
| title_short | On coercive variational integrals |
| title_sort | on coercive variational integrals |
| work_keys_str_mv | AT kristensenj oncoercivevariationalintegrals AT chenc oncoercivevariationalintegrals |