Overdetermined problems for the rotationally invariant Poisson equation in model manifolds
Abstract
We present rigidity results for overdetermined problems associated to the rotationally invariant Poisson equation -Δu = f(r) in a model manifold M with pole O. 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. Our results apply in particular to the three space forms with constant curvature.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Differential Geometry Research
Publication details
- Journal / source
- Journal of Differential Equations
- Volume
- 475
- Pages
- 114496–114496
- Publication date
- 18 May 2026
- Language
- EN