We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, in , for general obstacles . Our main result establishes the complete structure and regularity of the singular set. To prove it, we construct new monotonicity formulas of Monneau-type that extend those in those of Garofalo–Petrosyan to all .
Cite this article
Nicola Garofalo, Xavier Ros-Oton, Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian. Rev. Mat. Iberoam. 35 (2019), no. 5, pp. 1309–1365DOI 10.4171/RMI/1087