Unique continuation estimates for Baouendi--Grushin equations on cylinders
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909734057017344 |
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| author | Alphonse, Paul Seelmann, Albrecht |
| author_facet | Alphonse, Paul Seelmann, Albrecht |
| contents | We prove time-pointwise quantitative unique continuation estimates for the evolution operators associated to (fractional powers of) the Baouendi--Grushin operators on the cylinder $\mathbb{R}^d \times \mathbb{T}^d$. Corresponding spectral inequalities, relating for functions from spectral subspaces associated to finite energy intervals their $L^2$-norm on the whole cylinder to the $L^2$-norm on a suitable subset, and results on exact and approximate null-controllabilty are deduced. This extends and complements results obtained recently by the authors and by Jaming and Wang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unique continuation estimates for Baouendi--Grushin equations on cylinders Alphonse, Paul Seelmann, Albrecht Analysis of PDEs Optimization and Control Spectral Theory 35P05, 93B05, 35P10 We prove time-pointwise quantitative unique continuation estimates for the evolution operators associated to (fractional powers of) the Baouendi--Grushin operators on the cylinder $\mathbb{R}^d \times \mathbb{T}^d$. Corresponding spectral inequalities, relating for functions from spectral subspaces associated to finite energy intervals their $L^2$-norm on the whole cylinder to the $L^2$-norm on a suitable subset, and results on exact and approximate null-controllabilty are deduced. This extends and complements results obtained recently by the authors and by Jaming and Wang. |
| title | Unique continuation estimates for Baouendi--Grushin equations on cylinders |
| topic | Analysis of PDEs Optimization and Control Spectral Theory 35P05, 93B05, 35P10 |
| url | https://arxiv.org/abs/2401.17782 |