Remarks on the fine structure of the free boundary (the no-sign obstacle problem)

Abstract

We present a number of results inspired by the approach developed in a recent work by A. Figalli and J. Serra on the fine structure of the obstacle problem, which turns out to be partially effective in addressing the no-sign obstacle problem. However, we also highlight one or two central questions that remain open and appear to require different techniques not presently available to us.

12 pages