Speaker:
Dr. Stefano Borghini
- Department of Mathematics, Uppsala University
Tuesday, June 11, 2019
at
1:30 PM
We discuss overdetermined elliptic boundary value problems in the Euclidean space. We will focus in particular on the torsion problem, which consists in the study of pairs (Ω,u), where Ω⊂R^n is a bounded domain and u: Ω→R is a function with constant nonzero laplacian and such that u= 0 on the boundary ∂Ω. A celebrated result, proven by Serrin, states that, if the normal derivative ∂u/∂ν is constant on ∂Ω, then Ω is a ball and u is rotationally symmetric. After reviewing Serrin’s work, we will introduce and apply some recent geometric techniques to study the case where ∂Ω is disconnected and ∂u/∂ν is allowed to assume distinct values on different boundary components.
