Shigeru Sakaguchi

Rigidity for two-phase overdetermined problems in $\mathbb{S}^n$

In this paper, we study rigidity phenomena associated with a class of overdetermined two-phase problems on the $n$-dimensional sphere $\mathbb{S}^n$. Specifically, we analyze the solutions of coupled elliptic equations defined on a domain $\Omega \subset \mathbb{S}^n$ and its complement, subject to Dirichlet boundary c...