# name
Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian

# metadata.dc.description.abstract[].value
We study the singular part of the free boundary in the obstacle problem for the fractional Laplacian, $\min \left\{(-\Delta)^s u, u-\varphi\right\}=0$ in $\mathbb{R}^n$, for general obstacles $\varphi$. 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 $s \in(0,1)$.

# metadata.dc.publisher[].value
European Mathematical Society Publishing House

# metadata.dc.relation.ispartof[].value
Revista Matematica Iberoamericana, 2019, vol. 35, num. 5, p. 1309-1365

# metadata.dc.rights[].value
(c) European Mathematical Society Publishing House, 2019

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian