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In this note, we study a Serrin-type partially overdetermined problemproposed by Guo-Xia (Calc. Var. Partial Differential Equations 58: no. 160,2019. https://doi.org/10.1007/s00526-019-1603-3, and prove a rigidity resultthat characterizes capillary spherical caps in a half ball.

A characterization of capillary spherical caps by a partially overdetermined problem in a half ball