Zero modes and Dirac-(logarithmic) Sobolev-type inequalities
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909466370244608 |
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| author | Chatzakou, Marianna Kahler, Uwe Ruzhansky, Michael |
| author_facet | Chatzakou, Marianna Kahler, Uwe Ruzhansky, Michael |
| contents | We study the decay rate of the zero modes of the Dirac operator with a matrix-valued potential that is considered here without any regularity assumptions, compared to the existing literature. For the Dirac operator and for Clifford-valued functions we prove the $L^p$-$L^2$ Dirac Sobolev inequality with explicit constant, as well as the $L^p$-$L^q$ Dirac-Sobolev inequalities. We prove its logarithmic counterpart for $q=2$, extending it to its Gaussian version of Gross, as well as show Nash and Poincaré inequalities in this setting, with explicit values for constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zero modes and Dirac-(logarithmic) Sobolev-type inequalities Chatzakou, Marianna Kahler, Uwe Ruzhansky, Michael Analysis of PDEs We study the decay rate of the zero modes of the Dirac operator with a matrix-valued potential that is considered here without any regularity assumptions, compared to the existing literature. For the Dirac operator and for Clifford-valued functions we prove the $L^p$-$L^2$ Dirac Sobolev inequality with explicit constant, as well as the $L^p$-$L^q$ Dirac-Sobolev inequalities. We prove its logarithmic counterpart for $q=2$, extending it to its Gaussian version of Gross, as well as show Nash and Poincaré inequalities in this setting, with explicit values for constants. |
| title | Zero modes and Dirac-(logarithmic) Sobolev-type inequalities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.15132 |