A rigidity theorem for Kolmogorov-type operators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912102451511296 |
|---|---|
| author | Kogoj, Alessia E. Lanconelli, E. |
| author_facet | Kogoj, Alessia E. Lanconelli, E. |
| contents | Let $D\subseteq \mathbb{R}^n$, $n\geq 3$, be a bounded open set and let $x_0\in D$. Assume that the Newtonian potential of $D$ is proportional outside $D$ to the Newtonian potential of a mass concentrated at $\{x_0\}.$ Then $D$ is a Euclidean ball centered at $x_0$. This Theorem, proved by Aharonov, Shiffer and Zalcman in 1981, was extended to the caloric setting by Suzuki and Watson in 2001. In this note, we show that Suzuki--Watson Theorem is a particular case of a more general rigidity result related to a class of Kolmogorov-type PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A rigidity theorem for Kolmogorov-type operators Kogoj, Alessia E. Lanconelli, E. Analysis of PDEs 35H10, 35K65, 35K70, 53C24, 35K05, 35B99 Let $D\subseteq \mathbb{R}^n$, $n\geq 3$, be a bounded open set and let $x_0\in D$. Assume that the Newtonian potential of $D$ is proportional outside $D$ to the Newtonian potential of a mass concentrated at $\{x_0\}.$ Then $D$ is a Euclidean ball centered at $x_0$. This Theorem, proved by Aharonov, Shiffer and Zalcman in 1981, was extended to the caloric setting by Suzuki and Watson in 2001. In this note, we show that Suzuki--Watson Theorem is a particular case of a more general rigidity result related to a class of Kolmogorov-type PDEs. |
| title | A rigidity theorem for Kolmogorov-type operators |
| topic | Analysis of PDEs 35H10, 35K65, 35K70, 53C24, 35K05, 35B99 |
| url | https://arxiv.org/abs/2411.00961 |