Unique continuation at infinity: Carleman estimates on general warped cylinders
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911917358972928 |
|---|---|
| author | De Ponti, Nicolò Pigola, Stefano Veronelli, Giona |
| author_facet | De Ponti, Nicolò Pigola, Stefano Veronelli, Giona |
| contents | We obtain a vanishing result for solutions of the inequality $|Δu|\le q_1|u|+q_2|\nabla u|$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The appropriate decay condition at infinity on $u$ is related to the behavior of the potential functions $q_1$ and $q_2$ and to the asymptotic geometry of the end. The main ingredient is a new Carleman estimate of independent interest. Geometric applications to conformal deformations and to minimal graphs are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unique continuation at infinity: Carleman estimates on general warped cylinders De Ponti, Nicolò Pigola, Stefano Veronelli, Giona Analysis of PDEs Differential Geometry We obtain a vanishing result for solutions of the inequality $|Δu|\le q_1|u|+q_2|\nabla u|$ that decay to zero along a very general warped cylindrical end of a Riemannian manifold. The appropriate decay condition at infinity on $u$ is related to the behavior of the potential functions $q_1$ and $q_2$ and to the asymptotic geometry of the end. The main ingredient is a new Carleman estimate of independent interest. Geometric applications to conformal deformations and to minimal graphs are presented. |
| title | Unique continuation at infinity: Carleman estimates on general warped cylinders |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2401.12367 |