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.
A rigidity theorem for Kolmogorov-type operators
A. E. Kogoj
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In corso di stampa
Abstract
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.File in questo prodotto:
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