The Singular Set of Higher Dimensional Unstable Obstacle Type Problems

Abstract

In this paper we will investigate the singular points of the following unstable free boundary problem: {equation}\label{Eq} Δu= -χ_{\{u>0\}} \quad\quad\textrm{in} B_1(0) {equation} where $\ddot{I}{‡}_{\{u>0\}}$ is the characteristic function of the set $\{u>0\}$.