Domain characterization for Schrödinger operators with sub-quadratic singularity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917776470310912 |
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| author | Metafune, Giorgio Sobajima, Motohiro |
| author_facet | Metafune, Giorgio Sobajima, Motohiro |
| contents | We characterize the domain of the Schrödinger operators $S=-Δ+c|x|^{-α}$ in $L^p(\mathbb{R}^N)$, with $0<α<2$ and $c\in\mathbb{R}$. When $αp< N$, the domain characterization is essentially known and can be proved using different tools, for instance kernel estimates and potentials in the Kato class or in the reverse Hölder class. However,the other cases seem not to be known, so far.In this paper, we give the explicit description of the domain of $S$ for all range of parameters $p,α$ and $c$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Domain characterization for Schrödinger operators with sub-quadratic singularity Metafune, Giorgio Sobajima, Motohiro Analysis of PDEs 35J75, 35K67, 47D08 We characterize the domain of the Schrödinger operators $S=-Δ+c|x|^{-α}$ in $L^p(\mathbb{R}^N)$, with $0<α<2$ and $c\in\mathbb{R}$. When $αp< N$, the domain characterization is essentially known and can be proved using different tools, for instance kernel estimates and potentials in the Kato class or in the reverse Hölder class. However,the other cases seem not to be known, so far.In this paper, we give the explicit description of the domain of $S$ for all range of parameters $p,α$ and $c$. |
| title | Domain characterization for Schrödinger operators with sub-quadratic singularity |
| topic | Analysis of PDEs 35J75, 35K67, 47D08 |
| url | https://arxiv.org/abs/2409.09917 |