Construction of blowup solutions for Liouville systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914094439727104 |
|---|---|
| author | Cheng, Zetao Li, Haoyu Zhang, Lei |
| author_facet | Cheng, Zetao Li, Haoyu Zhang, Lei |
| contents | We study the following Liouville system defined on a flat torus \begin{equation} \left\{ \begin{array}{lr} -Δu_i=\sum_{j=1}^n a_{ij}ρ_j\Big(\frac{h_j e^{u_j}}{\int_Ωh_j e^{u_j}}-1\Big),\nonumber \\ u_j\in H_{per}^1(Ω)\mbox{ for }i\in I=\{1,\cdots,n\}\nonumber, \end{array} \right. \end{equation} where $h_j\in C^3(Ω)$, $h_j>0$, $ρ_j>0$ and $u=(u_1,..,u_n)$ is doubly periodic on $\partialΩ$. The matrix $A=(a_{ij})_{n\times n}$ satisfies certain properties. One central problem about Liouville systems is whether multi-bubble solutions do exist. In this work we present a comprehensive construction of multi-bubble solutions in the most general setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07467 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of blowup solutions for Liouville systems Cheng, Zetao Li, Haoyu Zhang, Lei Analysis of PDEs Mathematical Physics 35J47 58J90 We study the following Liouville system defined on a flat torus \begin{equation} \left\{ \begin{array}{lr} -Δu_i=\sum_{j=1}^n a_{ij}ρ_j\Big(\frac{h_j e^{u_j}}{\int_Ωh_j e^{u_j}}-1\Big),\nonumber \\ u_j\in H_{per}^1(Ω)\mbox{ for }i\in I=\{1,\cdots,n\}\nonumber, \end{array} \right. \end{equation} where $h_j\in C^3(Ω)$, $h_j>0$, $ρ_j>0$ and $u=(u_1,..,u_n)$ is doubly periodic on $\partialΩ$. The matrix $A=(a_{ij})_{n\times n}$ satisfies certain properties. One central problem about Liouville systems is whether multi-bubble solutions do exist. In this work we present a comprehensive construction of multi-bubble solutions in the most general setting. |
| title | Construction of blowup solutions for Liouville systems |
| topic | Analysis of PDEs Mathematical Physics 35J47 58J90 |
| url | https://arxiv.org/abs/2503.07467 |