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...

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Main Author: Alessia E. Kogoj
Format: Article
Language:English
Published: University of Bologna 2025-01-01
Series:Bruno Pini Mathematical Analysis Seminar
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Online Access:https://mathematicalanalysis.unibo.it/article/view/21058
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author Alessia E. Kogoj
author_facet Alessia E. Kogoj
author_sort Alessia E. Kogoj
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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.
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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