The structure of the regular part of the free boundary close to singularities in the obstacle problem

We prove the -- to the best knowledge of the authors -- first result on the fine asymptotic behavior of the regular part of the free boundary of the obstacle problem close to singularities. The result is motivated by our recent partial answer to a long standing conjecture and the first partial classification of global solutions of the obstacle problem with unbounded coincidence sets in higher dimensions.
Comment: arXiv admin note: substantial text overlap with arXiv:2005.04915