| Abstract: |
| Overdetermined problems for the rotationally invariant Poisson
equation $-\Delta u = f(r)$ in a Riemannian manifold with pole~$O$
have been recently investigated (arXiv:2602.18289) by Marcello Lucia
(New York), Pieralberto Sicbaldi (Granada) and the speaker. We give
conditions on~$f$ and on the boundary data implying that the
solution~$u$ is radial and the domain of the problem is a geodesic
ball centered at~$O$, or an annulus centered there. Our results hold,
in particular, in the three space forms with constant curvature.
Proofs are based on the comparison principle. |
|