Obstacle problems for integro-differential operators: Higher regularity of free boundaries
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...
| Authors: | ; |
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| Format: | Article |
| Status: | Accepted version |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/194137 |
| Online Access: | https://hdl.handle.net/2445/194137 |
| Access Level: | Open access |
| Keyword: | Operadors integrals Operadors diferencials Teoria d'operadors Equacions en derivades parcials Integral operators Differential operators Operator theory Partial differential equations |
| Summary: | 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 $k=1$ ). |
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