Generalized Strichartz estimates for the massive Dirac equation with critical potentials
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915579990900736 |
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| author | Cacciafesta, Federico Danesi, Elena Séré, Eric |
| author_facet | Cacciafesta, Federico Danesi, Elena Séré, Eric |
| contents | In this paper we prove generalized Strichartz estimates for the massive Dirac equation in the case of two critical potential perturbations, namely the $2d$ Aharonov-Bohm magnetic potential and the $3d$ Coulomb potential. The proof makes use of the relativistic Hankel transform introduced in previous works of Cacciafesta, Séré and Cacciafesta, Fanelli for the massless systems, and here adapted to the massive case: this allows for an explicit representation of the solutions, which reduces the analysis to the proof of suitable estimates on the generalized eigenfunctions of the operators. To the best of our knowledge, these are the first dispersive estimates for the massive Dirac equation with critical potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23283 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Strichartz estimates for the massive Dirac equation with critical potentials Cacciafesta, Federico Danesi, Elena Séré, Eric Analysis of PDEs 42B37, 35Q40, 35Q41 In this paper we prove generalized Strichartz estimates for the massive Dirac equation in the case of two critical potential perturbations, namely the $2d$ Aharonov-Bohm magnetic potential and the $3d$ Coulomb potential. The proof makes use of the relativistic Hankel transform introduced in previous works of Cacciafesta, Séré and Cacciafesta, Fanelli for the massless systems, and here adapted to the massive case: this allows for an explicit representation of the solutions, which reduces the analysis to the proof of suitable estimates on the generalized eigenfunctions of the operators. To the best of our knowledge, these are the first dispersive estimates for the massive Dirac equation with critical potentials. |
| title | Generalized Strichartz estimates for the massive Dirac equation with critical potentials |
| topic | Analysis of PDEs 42B37, 35Q40, 35Q41 |
| url | https://arxiv.org/abs/2510.23283 |