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In this note, we prove the uniqueness of blowups at singular points of theno-sign obstacle problem $\Delta u=\chi_{_{B_1\backslash \{u=|Du|=0\}}}\\text{in}\ B_1,$ thus give a positive answer to a problem raised in \cite[Notesof Chaper 7, page 149]{PSU12}.

A note on the singular set of the no-sign obstacle problem