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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2503.19154 |
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| _version_ | 1866918084554522624 |
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| author | Carrillo, José A. Fetecau, Razvan C. Park, Hansol |
| author_facet | Carrillo, José A. Fetecau, Razvan C. Park, Hansol |
| contents | We investigate the existence of ground states for a free energy functional on Cartan-Hadamard manifolds. The energy, which consists of an entropy and an interaction term, is associated to a macroscopic aggregation model that includes nonlinear diffusion and nonlocal interactions. We consider specifically the regime of fast diffusion, and establish necessary and sufficient conditions on the behaviour of the interaction potential for global energy minimizers to exist. We first consider the case of manifolds with constant bounds of sectional curvatures, then extend the results to manifolds with general curvature bounds. To establish our results we derive several new Carlson-Levin type inequalities for Cartan-Hadamard manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global minimizers for fast diffusion versus nonlocal interactions on negatively curved manifolds Carrillo, José A. Fetecau, Razvan C. Park, Hansol Analysis of PDEs Differential Geometry 35A15, 35B38, 39B62, 58J90 We investigate the existence of ground states for a free energy functional on Cartan-Hadamard manifolds. The energy, which consists of an entropy and an interaction term, is associated to a macroscopic aggregation model that includes nonlinear diffusion and nonlocal interactions. We consider specifically the regime of fast diffusion, and establish necessary and sufficient conditions on the behaviour of the interaction potential for global energy minimizers to exist. We first consider the case of manifolds with constant bounds of sectional curvatures, then extend the results to manifolds with general curvature bounds. To establish our results we derive several new Carlson-Levin type inequalities for Cartan-Hadamard manifolds. |
| title | Global minimizers for fast diffusion versus nonlocal interactions on negatively curved manifolds |
| topic | Analysis of PDEs Differential Geometry 35A15, 35B38, 39B62, 58J90 |
| url | https://arxiv.org/abs/2503.19154 |