Conformally Invariant Dirac Equation with Non-Local Nonlinearity
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_ | 1866908320171819008 |
|---|---|
| author | Maalaoui, Ali Martino, Vittorio Mbarki, Lamine |
| author_facet | Maalaoui, Ali Martino, Vittorio Mbarki, Lamine |
| contents | We study a conformally invariant equation involving the Dirac operator and a non-linearity of convolution type. This non-linearity is inspired from the conformal Einstein-Dirac problem in dimension 4. We first investigate the compactness, bubbling and energy quantization of the associated energy functional then we characterize the ground state solutions of the problem on the standard sphere. As a consequence, we prove an Aubin-type inequality that assures the existence of solutions to our problem and in particular the conformal Einstein-Dirac problem in dimension 4. Moreover, we investigate the effect of a linear perturbation to our problem, leading us to a Brezis-Nirenberg type result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformally Invariant Dirac Equation with Non-Local Nonlinearity Maalaoui, Ali Martino, Vittorio Mbarki, Lamine Differential Geometry Analysis of PDEs 53C18, 53C27, 58J55, 58J60 We study a conformally invariant equation involving the Dirac operator and a non-linearity of convolution type. This non-linearity is inspired from the conformal Einstein-Dirac problem in dimension 4. We first investigate the compactness, bubbling and energy quantization of the associated energy functional then we characterize the ground state solutions of the problem on the standard sphere. As a consequence, we prove an Aubin-type inequality that assures the existence of solutions to our problem and in particular the conformal Einstein-Dirac problem in dimension 4. Moreover, we investigate the effect of a linear perturbation to our problem, leading us to a Brezis-Nirenberg type result. |
| title | Conformally Invariant Dirac Equation with Non-Local Nonlinearity |
| topic | Differential Geometry Analysis of PDEs 53C18, 53C27, 58J55, 58J60 |
| url | https://arxiv.org/abs/2504.10779 |