Abatangelo, NicolaRos, Xavier2023-02-242023-02-242020-01-220001-8708https://hdl.handle.net/2445/194137We study the higher regularity of free boundaries in obstacle problems for integrodifferential operators. Our main result establishes that, once free boundaries are $C^{1, \alpha}$, then they are $C^{\infty}$. This completes the study of regular points, initiated in [5]. In order to achieve this, we need to establish optimal boundary regularity estimates for solutions to linear nonlocal equations in $C^{k, \alpha}$ domains. These new estimates are the core of our paper, and extend previously known results by Grubb (for $k=\infty$ ) and by the second author and Serra (for $k=1$ ).application/pdfengcc-by-nc-nd (c) Elsevier B.V., 2020https://creativecommons.org/licenses/by-nc-nd/4.0/Operadors integralsOperadors diferencialsTeoria d'operadorsEquacions en derivades parcialsIntegral operatorsDifferential operatorsOperator theoryPartial differential equationsinfo:eu-repo/semantics/article7078382023-02-24info:eu-repo/semantics/openAccess