On the uniqueness of variable coefficient Schrödinger equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910796516163584 |
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| author | Federico, Serena Li, Zongyuan Yu, Xueying |
| author_facet | Federico, Serena Li, Zongyuan Yu, Xueying |
| contents | We prove unique continuation properties for linear variable coefficient Schrödinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any cubic exponential rate at two different times must be identically zero. Assuming a transversally anisotropic type condition, we recover the sharp Gaussian (quadratic exponential) rate in the series of works by Escauriaza-Kenig-Ponce-Vega [14, 17, 18]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03740 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the uniqueness of variable coefficient Schrödinger equations Federico, Serena Li, Zongyuan Yu, Xueying Analysis of PDEs 35B60, 35B45, 35Q41 We prove unique continuation properties for linear variable coefficient Schrödinger equations with bounded real potentials. Under certain smallness conditions on the leading coefficients, we prove that solutions decaying faster than any cubic exponential rate at two different times must be identically zero. Assuming a transversally anisotropic type condition, we recover the sharp Gaussian (quadratic exponential) rate in the series of works by Escauriaza-Kenig-Ponce-Vega [14, 17, 18]. |
| title | On the uniqueness of variable coefficient Schrödinger equations |
| topic | Analysis of PDEs 35B60, 35B45, 35Q41 |
| url | https://arxiv.org/abs/2211.03740 |