Non-isoparametric Serrin domains of ${\mathbb{S}}^3$ with connected toric boundary

Andrea Bisterzo, Shigeru Sakaguchi

We investigate the overdetermined torsion problem $\begin{cases} -Δu = 1 & \text{in}\ Ω\\ u=0 & \text{on}\ \partial Ω\\ \frac{\partial u}{\partial ν}=\text{const.} & \text{on}\ \pa…