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On the functional ∫Ωf + ∫Ω*g
- Source :
- Advanced Nonlinear Studies, Vol 24, Iss 1, Pp 29-43 (2024)
- Publication Year :
- 2024
- Publisher :
- De Gruyter, 2024.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 21690375
- Volume :
- 24
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Advanced Nonlinear Studies
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.925d5e61766544a2b06ac9720dab2593
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/ans-2023-0105