On some singularly perturbed elliptic systems modeling partial segregation: uniform Hölder estimates and basic properties of the limits
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913507721609216 |
|---|---|
| author | Soave, Nicola Terracini, Susanna |
| author_facet | Soave, Nicola Terracini, Susanna |
| contents | We prove uniform Hölder estimates in a class of singularly perturbed competition-diffusion elliptic systems, with the particular feature that the interactions between the components occur three by three (ternary interactions). These systems are associated to the minimization of Gross-Pitaevski energies modeling ternary mixture of ultracold gases and other multicomponent liquids and gases. We address the question whether this regularity holds uniformly throughout the approximation process up to the limiting profiles, answering positively. A very relevant feature of limiting profiles in this process is that they are only partially segregated, giving rise to new phenomena of geometric pattern formation and optimal regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11976 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On some singularly perturbed elliptic systems modeling partial segregation: uniform Hölder estimates and basic properties of the limits Soave, Nicola Terracini, Susanna Analysis of PDEs We prove uniform Hölder estimates in a class of singularly perturbed competition-diffusion elliptic systems, with the particular feature that the interactions between the components occur three by three (ternary interactions). These systems are associated to the minimization of Gross-Pitaevski energies modeling ternary mixture of ultracold gases and other multicomponent liquids and gases. We address the question whether this regularity holds uniformly throughout the approximation process up to the limiting profiles, answering positively. A very relevant feature of limiting profiles in this process is that they are only partially segregated, giving rise to new phenomena of geometric pattern formation and optimal regularity. |
| title | On some singularly perturbed elliptic systems modeling partial segregation: uniform Hölder estimates and basic properties of the limits |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.11976 |