Nodal set for the Schrödinger equation under a local growth condition
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913960291205120 |
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| author | Kukavica, Igor Li, Linfeng |
| author_facet | Kukavica, Igor Li, Linfeng |
| contents | We address the upper bound on the size of the nodal set for a solution $w$ of the Schrödinger equation $Δw= W\cdot \nabla w+V w$ in an open set in $\mathbb{R}^n$, where the coefficients belong to certain Sobolev spaces. Assuming a local doubling condition for the solution $w$, we establish an upper bound on the $(n-1)$-dimensional Hausdorff measure of the nodal set, with the bound depending algebraically on the Sobolev norms of $W$ and $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nodal set for the Schrödinger equation under a local growth condition Kukavica, Igor Li, Linfeng Analysis of PDEs We address the upper bound on the size of the nodal set for a solution $w$ of the Schrödinger equation $Δw= W\cdot \nabla w+V w$ in an open set in $\mathbb{R}^n$, where the coefficients belong to certain Sobolev spaces. Assuming a local doubling condition for the solution $w$, we establish an upper bound on the $(n-1)$-dimensional Hausdorff measure of the nodal set, with the bound depending algebraically on the Sobolev norms of $W$ and $V$. |
| title | Nodal set for the Schrödinger equation under a local growth condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.19600 |