Document type
ArticleVersion
Accepted versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/194137
Obstacle problems for integro-differential operators: Higher regularity of free boundaries
Journal Title
Authors
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
We 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 $k=1$ ).
Subject (English)
Citation
Citation
ABATANGELO, Nicola and ROS, Xavier. Obstacle problems for integro-differential operators: Higher regularity of free boundaries. Advances in Mathematics. 2020. Vol. 360, num. Article 106931, pags. 106931. ISSN 0001-8708. [consulted: 13 of June of 2026]. Available at: https://hdl.handle.net/2445/194137