Existence of Solutions to a super-Liouville equation with Boundary Conditions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929587317899264 |
|---|---|
| author | Han, Mingyang Wu, Ruijun Zhou, Chunqin |
| author_facet | Han, Mingyang Wu, Ruijun Zhou, Chunqin |
| contents | In this paper, we study the existence of solutions to a type of super-Liouville equation on the compact Riemannian surface $M$ with boundary and with its Euler characteristic $χ(M)<0$. The boundary condition couples a Neumann condition for functions and a chirality boundary condition for spinors. Due to the generality of the equation, we introduce a weighted Dirac operator based on the solution to a related Liouville equation. Then we construct a Nehari manifold according to the spectral decomposition of the weighted Dirac operator, and use minimax theory on this Nehari manifold to show the existence of the non-trivial solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of Solutions to a super-Liouville equation with Boundary Conditions Han, Mingyang Wu, Ruijun Zhou, Chunqin Analysis of PDEs Differential Geometry In this paper, we study the existence of solutions to a type of super-Liouville equation on the compact Riemannian surface $M$ with boundary and with its Euler characteristic $χ(M)<0$. The boundary condition couples a Neumann condition for functions and a chirality boundary condition for spinors. Due to the generality of the equation, we introduce a weighted Dirac operator based on the solution to a related Liouville equation. Then we construct a Nehari manifold according to the spectral decomposition of the weighted Dirac operator, and use minimax theory on this Nehari manifold to show the existence of the non-trivial solutions. |
| title | Existence of Solutions to a super-Liouville equation with Boundary Conditions |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2411.06930 |