On the strong unique continuation property for the Dirac operator
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915275432001536 |
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| author | Cassano, Biagio |
| author_facet | Cassano, Biagio |
| contents | In [DO99,KY99], the strong unique continuation property from the origin is established for $H_{loc}^1$-solutions to the massless Dirac differential inequality $|{D}_n u | \leq \frac{C}{|x|}|u|$, in dimension $n\geq 2$ and with $C<\frac12$. We show that $\frac12$ is the largest possibile constant in this result, providing an example in $\mathbb{R}^2$ of a (non-trivial) solution of the inequality. Also, we show properties of unique continuation from the origin for solutions to the inequality $|D_n u | \leq \frac{C}{ |x|^γ}|u|$, for $γ>1$, $C>0$. Finally, we establish the strong unique continuation property for the Dirac operator from the point at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the strong unique continuation property for the Dirac operator Cassano, Biagio Analysis of PDEs Mathematical Physics 35B60, 35Q40, 35B99 In [DO99,KY99], the strong unique continuation property from the origin is established for $H_{loc}^1$-solutions to the massless Dirac differential inequality $|{D}_n u | \leq \frac{C}{|x|}|u|$, in dimension $n\geq 2$ and with $C<\frac12$. We show that $\frac12$ is the largest possibile constant in this result, providing an example in $\mathbb{R}^2$ of a (non-trivial) solution of the inequality. Also, we show properties of unique continuation from the origin for solutions to the inequality $|D_n u | \leq \frac{C}{ |x|^γ}|u|$, for $γ>1$, $C>0$. Finally, we establish the strong unique continuation property for the Dirac operator from the point at infinity. |
| title | On the strong unique continuation property for the Dirac operator |
| topic | Analysis of PDEs Mathematical Physics 35B60, 35Q40, 35B99 |
| url | https://arxiv.org/abs/2505.03421 |