On a rigidity result for Kolmogorov-type operators
Let D be a bounded open subset of ℝN and let z0 be a point of D. Assume that the Newtonian potential of D is proportional outside D to the potential of a mass concentrated at z0. Then D is a Euclidean ball centred at z0. This theorem, proved by Aharonov, Schiffer and Zalcman in 1981, was extended to...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Bologna
2025-01-01
|
| Series: | Bruno Pini Mathematical Analysis Seminar |
| Subjects: | |
| Online Access: | https://mathematicalanalysis.unibo.it/article/view/21058 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849221733945442304 |
|---|---|
| author | Alessia E. Kogoj |
| author_facet | Alessia E. Kogoj |
| author_sort | Alessia E. Kogoj |
| collection | DOAJ |
| description | Let D be a bounded open subset of ℝN and let z0 be a point of D. Assume that the Newtonian potential of D is proportional outside D to the potential of a mass concentrated at z0. Then D is a Euclidean ball centred at z0. This theorem, proved by Aharonov, Schiffer and Zalcman in 1981, was extended to the caloric setting by Suzuki and Watson in 2001. In this note, we extend the Suzuki–Watson Theorem to a class of hypoellliptic operators of Kolmogorov-type. |
| format | Article |
| id | doaj-art-9874d468ddf747a1b5a8dcb71e62e5b5 |
| institution | Kabale University |
| issn | 2240-2829 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj-art-9874d468ddf747a1b5a8dcb71e62e5b52025-01-15T16:52:44ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292025-01-011519811110.6092/issn.2240-2829/2105819432On a rigidity result for Kolmogorov-type operatorsAlessia E. Kogoj0Dipartimento di Scienze Pure e Applicate, Università degli Studi di Urbino Carlo BoLet D be a bounded open subset of ℝN and let z0 be a point of D. Assume that the Newtonian potential of D is proportional outside D to the potential of a mass concentrated at z0. Then D is a Euclidean ball centred at z0. This theorem, proved by Aharonov, Schiffer and Zalcman in 1981, was extended to the caloric setting by Suzuki and Watson in 2001. In this note, we extend the Suzuki–Watson Theorem to a class of hypoellliptic operators of Kolmogorov-type.https://mathematicalanalysis.unibo.it/article/view/21058degenerate parabolic equationskolmogorov-type operatorshypoelliptic operatorsrigidity propertiesinverse problems |
| spellingShingle | Alessia E. Kogoj On a rigidity result for Kolmogorov-type operators Bruno Pini Mathematical Analysis Seminar degenerate parabolic equations kolmogorov-type operators hypoelliptic operators rigidity properties inverse problems |
| title | On a rigidity result for Kolmogorov-type operators |
| title_full | On a rigidity result for Kolmogorov-type operators |
| title_fullStr | On a rigidity result for Kolmogorov-type operators |
| title_full_unstemmed | On a rigidity result for Kolmogorov-type operators |
| title_short | On a rigidity result for Kolmogorov-type operators |
| title_sort | on a rigidity result for kolmogorov type operators |
| topic | degenerate parabolic equations kolmogorov-type operators hypoelliptic operators rigidity properties inverse problems |
| url | https://mathematicalanalysis.unibo.it/article/view/21058 |
| work_keys_str_mv | AT alessiaekogoj onarigidityresultforkolmogorovtypeoperators |