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

In this note, we prove the uniqueness of blowups at singular points of the no-sign obstacle problem $Δu=χ_{_{B_1\backslash \{u=|Du|=0\}}}\ \text{in}\ B_1,$ thus give a positive answer to a problem raised in \cite[Notes of Chaper 7, page 149]{PSU12}.

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