Existence of ground states for free energies on the hyperbolic space
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929492841201664 |
|---|---|
| author | Carrillo, José A. Fetecau, Razvan C. Park, Hansol |
| author_facet | Carrillo, José A. Fetecau, Razvan C. Park, Hansol |
| contents | We investigate a free energy functional that arises in aggregation-diffusion phenomena modelled by nonlocal interactions and local repulsion on the hyperbolic space $\bbh^\dm$. The free energy consists of two competing terms: an entropy, corresponding to slow nonlinear diffusion, that favours spreading, and an attractive interaction potential energy that favours aggregation. We establish necessary and sufficient conditions on the interaction potential for ground states to exist on the hyperbolic space $\bbh^\dm$. To prove our results we derived several Hardy-Littlewood-Sobolev (HLS)-type inequalities on general Cartan-Hadamard manifolds of bounded curvature, which have an interest in their own. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06022 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of ground states for free energies on the hyperbolic space Carrillo, José A. Fetecau, Razvan C. Park, Hansol Analysis of PDEs Differential Geometry 35A15, 35B38, 39B62, 58J90 We investigate a free energy functional that arises in aggregation-diffusion phenomena modelled by nonlocal interactions and local repulsion on the hyperbolic space $\bbh^\dm$. The free energy consists of two competing terms: an entropy, corresponding to slow nonlinear diffusion, that favours spreading, and an attractive interaction potential energy that favours aggregation. We establish necessary and sufficient conditions on the interaction potential for ground states to exist on the hyperbolic space $\bbh^\dm$. To prove our results we derived several Hardy-Littlewood-Sobolev (HLS)-type inequalities on general Cartan-Hadamard manifolds of bounded curvature, which have an interest in their own. |
| title | Existence of ground states for free energies on the hyperbolic space |
| topic | Analysis of PDEs Differential Geometry 35A15, 35B38, 39B62, 58J90 |
| url | https://arxiv.org/abs/2409.06022 |