Study of polyconvexity in some problems in the calculus of variations
| dc.contributor.author | Merabet, Ibrahim | |
| dc.date.accessioned | 2025-06-30T09:15:44Z | |
| dc.date.available | 2025-06-30T09:15:44Z | |
| dc.date.issued | 2025-04-17 | |
| dc.description.abstract | This study seeks to investigate the concept of symmetric polyconvex functions in higher-dimensional spaces. By advancing the methodology introduced by Boussaid et al. for two-dimensional and three-dimensional cases, we introduce an innovative characterization of symmetric polyconvex functions in higher dimensions. Our principal fiding reveals that the requisite condition for symmetric polyconvexity of a function f is its ability to be formulated as a convex function that incorporates the matrix and its second-order minors, exhibiting a non-increasing tendency in a specifi sense with respect to the second-order minor variable. Additionally, we propose and scrutinize the concept of S-positive semi-defiite matrices, which is crucial to our characterization. This new characterization also enables the identifiation of the class of symmetric polyconvex quadratic forms and demonstrates the absence of non-trivial symmetric poly-affi functions. | en_US |
| dc.identifier.uri | http://dspace.univ-chlef.dz/handle/123456789/2130 | |
| dc.publisher | Boussaid Omar / Kainane-Mezadek Abdelatif | en_US |
| dc.title | Study of polyconvexity in some problems in the calculus of variations | en_US |
| dc.title.alternative | Thesis Submitted in Fulfi lment of the Requirements for the Degree of L.M.D. Doctorate in Mathematics | en_US |
| dc.type | Thesis | en_US |