Special Session 65: Geometry of PDEs on Manifolds and Nilpotent Lie Groups
Symmetry and rigidity results for Serrin`s overdetermined type problems in weighted Riemannian manifolds
Giulio Ciraolo
University of Milan Italy
Co-Author(s): Laura Accornero
Abstract:
We consider the classical Serrin's overdetermined boundary value problem in a weighted Riemannian manifold. Under suitable assumptions, we prove that the existence of a solution implies that the domain must be isometric to an Euclidean ball, also providing a rigidity result on the underlying manifold.