Resumen de Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian

Nicola Garofalo, Xavier Ros

• We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, min{(−Δ)su,u−φ}=0 in Rn, for general obstacles φ. 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 s∈(0,1).