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

Shibing Chen; Yibin Feng; Yuanyuan Li

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arXiv · 2204.11426

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

Shibing Chen·Yibin Feng·Yuanyuan Li

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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}.

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Shibing Chen, Yibin Feng, Yuanyuan Li. 2022-04-25. A note on the singular set of the no-sign obstacle problem. https://arxiv.org/abs/2204.11426

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