English

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

Analysis of PDEs 2022-08-26 v2

Abstract

In this note, we prove the uniqueness of blowups at singular points of the no-sign obstacle problem Δu=χB1\{u=Du=0} in B1,\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}.

Keywords

Cite

@article{arxiv.2204.11426,
  title  = {A note on the singular set of the no-sign obstacle problem},
  author = {Shibing Chen and Yibin Feng and Yuanyuan Li},
  journal= {arXiv preprint arXiv:2204.11426},
  year   = {2022}
}