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

Abstract

In this note, we prove the uniqueness of blowups at singular points of the no-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[Notes of Chaper 7, page 149]{PSU12}.