Garofalo, NicolaRos, Xavier2023-02-232023-02-232019-06-050213-2230https://hdl.handle.net/2445/194048We 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 $s \in(0,1)$.57 p.application/pdfeng(c) European Mathematical Society Publishing House, 2019Operadors diferencials parcialsTeoria d'operadorsEquacions en derivades parcialsProcessos estocàsticsPartial differential operatorsOperator theoryPartial differential equationsStochastic processesinfo:eu-repo/semantics/article7085732023-02-23info:eu-repo/semantics/openAccess