Let D ⊆ Rn, n ≥ 3, be a bounded open set and let x0 ∈ D. Assume that the Newtonian potential of D is proportional outside D to the Newtonian potential of a mass concentrated at {x0}. Then D is a Euclidean ball centered at x0. 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 show that Suzuki–Watson Theorem is a particular case of a more general rigidity result related to a class of Kolmogorov-type PDEs.
