Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization
We consider a functional of the type F(u,Ω)=∫ΩF(Dku(x))dx on the Dirichlet class, where F is a continuous function and Ω is an open bounded set of Rn with a Lipschitz boundary. We prove that coercivity and mean coercivity are equivalent under growth conditions, and further we prove that mean coerciv...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Springer Nature
2025
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/118384/ http://psasir.upm.edu.my/id/eprint/118384/1/118384.pdf |
| _version_ | 1848867503977005056 |
|---|---|
| author | He, Xiaoying Chen, Chuei Yee |
| author_facet | He, Xiaoying Chen, Chuei Yee |
| author_sort | He, Xiaoying |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We consider a functional of the type F(u,Ω)=∫ΩF(Dku(x))dx on the Dirichlet class, where F is a continuous function and Ω is an open bounded set of Rn with a Lipschitz boundary. We prove that coercivity and mean coercivity are equivalent under growth conditions, and further we prove that mean coercivity and quasiconvexity are equivalent. Subsequently, we deduce that F(u,Ω) has a minimum under the condition that the integrand F satisfies the growth condition and mean coercivity. |
| first_indexed | 2025-11-15T14:37:32Z |
| format | Article |
| id | upm-118384 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:37:32Z |
| publishDate | 2025 |
| publisher | Springer Nature |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1183842025-07-09T03:06:43Z http://psasir.upm.edu.my/id/eprint/118384/ Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization He, Xiaoying Chen, Chuei Yee We consider a functional of the type F(u,Ω)=∫ΩF(Dku(x))dx on the Dirichlet class, where F is a continuous function and Ω is an open bounded set of Rn with a Lipschitz boundary. We prove that coercivity and mean coercivity are equivalent under growth conditions, and further we prove that mean coercivity and quasiconvexity are equivalent. Subsequently, we deduce that F(u,Ω) has a minimum under the condition that the integrand F satisfies the growth condition and mean coercivity. Springer Nature 2025-02-24 Article PeerReviewed text en cc_by_nc_nd_4 http://psasir.upm.edu.my/id/eprint/118384/1/118384.pdf He, Xiaoying and Chen, Chuei Yee (2025) Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization. Journal of Inequalities and Applications, 2025 (1). art. no. 21. pp. 1-13. ISSN 1025-5834; eISSN: 1029-242X https://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-025-03267-w 10.1186/s13660-025-03267-w |
| spellingShingle | He, Xiaoying Chen, Chuei Yee Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization |
| title | Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization |
| title_full | Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization |
| title_fullStr | Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization |
| title_full_unstemmed | Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization |
| title_short | Equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization |
| title_sort | equivalence of coercivity and mean coercivity in higher-order variational integrals with application to minimization |
| url | http://psasir.upm.edu.my/id/eprint/118384/ http://psasir.upm.edu.my/id/eprint/118384/ http://psasir.upm.edu.my/id/eprint/118384/ http://psasir.upm.edu.my/id/eprint/118384/1/118384.pdf |