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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2112.04457 |
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| _version_ | 1866911402651811840 |
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| author | Enciso, Alberto Shao, Arick Vergara, Bruno |
| author_facet | Enciso, Alberto Shao, Arick Vergara, Bruno |
| contents | We consider heat operators on a convex domain $Ω$, with a critically singular potential that diverges as the inverse square of the distance to the boundary of $Ω$. We establish a general boundary controllability result for such operators in all dimensions, in particular providing the first such result in more than one spatial dimension. The key step in the proof is a novel global Carleman estimate that captures both the appropriate boundary conditions and the $H^1$-energy for this problem. The estimate is derived by combining two intermediate Carleman inequalities with distinct and carefully constructed weights involving non-smooth powers of the boundary distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_04457 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates Enciso, Alberto Shao, Arick Vergara, Bruno Analysis of PDEs We consider heat operators on a convex domain $Ω$, with a critically singular potential that diverges as the inverse square of the distance to the boundary of $Ω$. We establish a general boundary controllability result for such operators in all dimensions, in particular providing the first such result in more than one spatial dimension. The key step in the proof is a novel global Carleman estimate that captures both the appropriate boundary conditions and the $H^1$-energy for this problem. The estimate is derived by combining two intermediate Carleman inequalities with distinct and carefully constructed weights involving non-smooth powers of the boundary distance. |
| title | Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2112.04457 |