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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 $Ω\subset \mathbb{S}^n$ and its complement, subject to Dirich
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