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Title: | Obstacle problems for integro-differential operators: Higher regularity of free boundaries |
Author: | Abatangelo, Nicola Ros, Xavier |
Keywords: | Operadors integrals Operadors diferencials Teoria d'operadors Equacions en derivades parcials Integral operators Differential operators Operator theory Partial differential equations |
Issue Date: | 22-Jan-2020 |
Publisher: | Elsevier B.V. |
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 $k=1$ ). |
Note: | Versió postprint del document publicat a: https://doi.org/10.1016/j.aim.2019.106931 |
It is part of: | Advances in Mathematics, 2020, vol. 360, num. Article 106931, p. 106931 |
URI: | http://hdl.handle.net/2445/194137 |
Related resource: | https://doi.org/10.1016/j.aim.2019.106931 |
ISSN: | 0001-8708 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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