On the functional ∫Ωf + ∫Ω*g
In this paper, we consider a class of functionals subject to a duality restriction. The functional is of the form J(Ω,Ω*)=∫Ωf+∫Ω*g $\mathcal{J}\left({\Omega},{{\Omega}}^{{\ast}}\right)={\int }_{{\Omega}}f+{\int }_{{{\Omega}}^{{\ast}}}g$ , where f, g are given nonnegative functions in a manifold. The...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-03-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2023-0105 |
| _version_ | 1797219193863536640 |
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| author | Guang Qiang Li Qi-Rui Wang Xu-Jia |
| author_facet | Guang Qiang Li Qi-Rui Wang Xu-Jia |
| author_sort | Guang Qiang |
| collection | DOAJ |
| description | In this paper, we consider a class of functionals subject to a duality restriction. The functional is of the form J(Ω,Ω*)=∫Ωf+∫Ω*g
$\mathcal{J}\left({\Omega},{{\Omega}}^{{\ast}}\right)={\int }_{{\Omega}}f+{\int }_{{{\Omega}}^{{\ast}}}g$
, where f, g are given nonnegative functions in a manifold. The duality is a relation α(x, y) ≤ 0 ∀ x ∈ Ω, y ∈ Ω*, for a suitable function α. This model covers several geometric and physical applications. In this paper we review two topological methods introduced in the study of the functional, and discuss possible extensions of the methods to related problems. |
| first_indexed | 2024-04-24T12:29:46Z |
| format | Article |
| id | doaj.art-925d5e61766544a2b06ac9720dab2593 |
| institution | Directory Open Access Journal |
| issn | 2169-0375 |
| language | English |
| last_indexed | 2024-04-24T12:29:46Z |
| publishDate | 2024-03-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-925d5e61766544a2b06ac9720dab25932024-04-08T07:35:24ZengDe GruyterAdvanced Nonlinear Studies2169-03752024-03-01241294310.1515/ans-2023-0105On the functional ∫Ωf + ∫Ω*gGuang Qiang0Li Qi-Rui1Wang Xu-Jia2Mathematical Sciences Institute, The Australian National University, Canberra, ACT2601, AustraliaSchool of Mathematical Sciences, Zhejiang University, Hangzhou310027, ChinaMathematical Sciences Institute, The Australian National University, Canberra, ACT2601, AustraliaIn this paper, we consider a class of functionals subject to a duality restriction. The functional is of the form J(Ω,Ω*)=∫Ωf+∫Ω*g $\mathcal{J}\left({\Omega},{{\Omega}}^{{\ast}}\right)={\int }_{{\Omega}}f+{\int }_{{{\Omega}}^{{\ast}}}g$ , where f, g are given nonnegative functions in a manifold. The duality is a relation α(x, y) ≤ 0 ∀ x ∈ Ω, y ∈ Ω*, for a suitable function α. This model covers several geometric and physical applications. In this paper we review two topological methods introduced in the study of the functional, and discuss possible extensions of the methods to related problems.https://doi.org/10.1515/ans-2023-0105minkowski type problemgeometric flowvariational methodprimary 35j20, 35k96secondary 53a07 |
| spellingShingle | Guang Qiang Li Qi-Rui Wang Xu-Jia On the functional ∫Ωf + ∫Ω*g Advanced Nonlinear Studies minkowski type problem geometric flow variational method primary 35j20, 35k96 secondary 53a07 |
| title | On the functional ∫Ωf + ∫Ω*g |
| title_full | On the functional ∫Ωf + ∫Ω*g |
| title_fullStr | On the functional ∫Ωf + ∫Ω*g |
| title_full_unstemmed | On the functional ∫Ωf + ∫Ω*g |
| title_short | On the functional ∫Ωf + ∫Ω*g |
| title_sort | on the functional ∫ωf ∫ω g |
| topic | minkowski type problem geometric flow variational method primary 35j20, 35k96 secondary 53a07 |
| url | https://doi.org/10.1515/ans-2023-0105 |
| work_keys_str_mv | AT guangqiang onthefunctionalōfōg AT liqirui onthefunctionalōfōg AT wangxujia onthefunctionalōfōg |