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: | ; |
|---|---|
| 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 |
| _version_ | 1878738024515239937 |
|---|---|
| author | Abatangelo, Nicola |
| author2 | Ros, Xavier |
| author2_role | author |
| author_browse | Abatangelo, Nicola Ros, Xavier |
| author_facet | Abatangelo, Nicola Ros, Xavier |
| author_role | author |
| collection | Recercat. Dipósit de la Recerca de Catalunya |
| description | 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 $k=1$ ). |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_a880e7685acdbbb7cf00a93b7511cedf |
| institution | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| instname_str | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:recercat.cat:2445/194137 |
| publishDate | 2020 |
| publishDateSort | 2020 |
| publisher | Elsevier B.V. |
| publisherStr | Elsevier B.V. |
| reponame_str | Recercat. Dipósit de la Recerca de Catalunya |
| spelling | Obstacle problems for integro-differential operators: Higher regularity of free boundaries Abatangelo, Nicola Ros, Xavier Operadors integrals Operadors diferencials Teoria d'operadors Equacions en derivades parcials Integral operators Differential operators Operator theory Partial differential equations 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 $k=1$ ). Elsevier B.V. https://hdl.handle.net/2445/194137 |
| spellingShingle | Obstacle problems for integro-differential operators: Higher regularity of free boundaries Abatangelo, Nicola Operadors integrals Operadors diferencials Teoria d'operadors Equacions en derivades parcials Integral operators Differential operators Operator theory Partial differential equations |
| status_str | acceptedVersion |
| title | Obstacle problems for integro-differential operators: Higher regularity of free boundaries |
| title_full | Obstacle problems for integro-differential operators: Higher regularity of free boundaries |
| title_fullStr | Obstacle problems for integro-differential operators: Higher regularity of free boundaries |
| title_full_unstemmed | Obstacle problems for integro-differential operators: Higher regularity of free boundaries |
| title_short | Obstacle problems for integro-differential operators: Higher regularity of free boundaries |
| title_sort | Obstacle problems for integro-differential operators: Higher regularity of free boundaries |
| topic | Operadors integrals Operadors diferencials Teoria d'operadors Equacions en derivades parcials Integral operators Differential operators Operator theory Partial differential equations |
| topic_facet | Operadors integrals Operadors diferencials Teoria d'operadors Equacions en derivades parcials Integral operators Differential operators Operator theory Partial differential equations |
| url | https://hdl.handle.net/2445/194137 |