Unique continuation for Schr{ö}dinger operators with partially Gevrey coefficients
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917575951122432 |
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| author | Filippas, Spyridon Laurent, Camille Léautaud, Matthieu |
| author_facet | Filippas, Spyridon Laurent, Camille Léautaud, Matthieu |
| contents | We prove a local unique continuation result for Schr\''odinger operators with time independent Lipschitz metrics and lower order terms which are Gevrey 2 in time and bounded in space. This implies global unique continuation from any open set in a connected Riemannian manifold. These results relax in the same geometric setting the analyticity assumption in time of the Tataru-Robbiano-Zuily-H\''ormander theorem for these operators. The proof is based on (i) a Tataru-Robbiano-Zuily-H\''ormander type Carleman estimate with a nonlocal weight adapted to the anisotropy of the Schr\''odinger operator and (ii) the description of the conjugation of the Schr\''odinger operator with Gevrey coefficients by this nonlocal weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14820 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unique continuation for Schr{ö}dinger operators with partially Gevrey coefficients Filippas, Spyridon Laurent, Camille Léautaud, Matthieu Analysis of PDEs Optimization and Control We prove a local unique continuation result for Schr\''odinger operators with time independent Lipschitz metrics and lower order terms which are Gevrey 2 in time and bounded in space. This implies global unique continuation from any open set in a connected Riemannian manifold. These results relax in the same geometric setting the analyticity assumption in time of the Tataru-Robbiano-Zuily-H\''ormander theorem for these operators. The proof is based on (i) a Tataru-Robbiano-Zuily-H\''ormander type Carleman estimate with a nonlocal weight adapted to the anisotropy of the Schr\''odinger operator and (ii) the description of the conjugation of the Schr\''odinger operator with Gevrey coefficients by this nonlocal weight. |
| title | Unique continuation for Schr{ö}dinger operators with partially Gevrey coefficients |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2401.14820 |