Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian.
Resumen:
We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian (−Δ)s in a Lipschitz bounded domain Ω⊂Rn satisfying the exterior ball condition. The weight is a power of the distance to the boundary ∂Ω of Ω that accounts for the singular boundary behavior of the solution for any 0
| 2019 | |
| Juan Pablo Borthagaray ha sido financiado en parte por la subvención DMS-1411808 de la NSF. | |
|
Obstacle problem Free boundaries Finite elements Fractional diffusion Weighted Sobolev spaces Graded meshes |
|
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47766 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1872865413883232256 |
|---|---|
| author | Borthagaray, Juan Pablo |
| author2 | Nochetto, Ricardo H. Salgado, Abner J. |
| author2_role | author author |
| author_facet | Borthagaray, Juan Pablo Nochetto, Ricardo H. Salgado, Abner J. |
| author_role | author |
| bitstream.checksum.fl_str_mv | 6429389a7df7277b72b7924fdc7d47a9 a006180e3f5b2ad0b88185d14284c0e0 5499c15bd6b32c37160bfba5f71ab0a0 13adb202270a5f7cee03e795b33133c4 38a39ace11f8d3e1f1c1a80034eb1b7c |
| bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 MD5 MD5 MD5 |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Borthagaray Juan Pablo, Universidad de la República (Uruguay). Facultad de Ingeniería. Nochetto Ricardo H., University of Maryland, USA Salgado Abner J., University of Tennessee, USA |
| dc.creator.none.fl_str_mv | Borthagaray, Juan Pablo Nochetto, Ricardo H. Salgado, Abner J. |
| dc.date.accessioned.none.fl_str_mv | 2024-12-26T15:19:34Z |
| dc.date.available.none.fl_str_mv | 2024-12-26T15:19:34Z |
| dc.date.issued.none.fl_str_mv | 2019 |
| dc.description.abstract.none.fl_txt_mv | We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian (−Δ)s in a Lipschitz bounded domain Ω⊂Rn satisfying the exterior ball condition. The weight is a power of the distance to the boundary ∂Ω of Ω that accounts for the singular boundary behavior of the solution for any 0<s<1. These bounds then serve us as a guide in the design and analysis of a finite element scheme over graded meshes for any dimension n, which is optimal for n=2. |
| dc.description.sponsorship.none.fl_txt_mv | Juan Pablo Borthagaray ha sido financiado en parte por la subvención DMS-1411808 de la NSF. |
| dc.format.extent.es.fl_str_mv | 26 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Borthagaray, J, Nochetto, R y Salgado, A. Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. Mathematical Models and Methods in Applied Sciences [preprint], 2019, 29(14), 2679-2717 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/47766 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.relation.none.fl_str_mv | Mathematical Models and Methods in Applied Sciences, 2019, 29(14), 2679-2717. |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Obstacle problem Free boundaries Finite elements Fractional diffusion Weighted Sobolev spaces Graded meshes |
| dc.title.none.fl_str_mv | Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian (−Δ)s in a Lipschitz bounded domain Ω⊂Rn satisfying the exterior ball condition. The weight is a power of the distance to the boundary ∂Ω of Ω that accounts for the singular boundary behavior of the solution for any 0<s<1. These bounds then serve us as a guide in the design and analysis of a finite element scheme over graded meshes for any dimension n, which is optimal for n=2. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_480bcb37be5b6a98ff2d02dd2e30ea40 |
| identifier_str_mv | Borthagaray, J, Nochetto, R y Salgado, A. Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. Mathematical Models and Methods in Applied Sciences [preprint], 2019, 29(14), 2679-2717 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/47766 |
| publishDate | 2019 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | karina.camps@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Borthagaray Juan Pablo, Universidad de la República (Uruguay). Facultad de Ingeniería.Nochetto Ricardo H., University of Maryland, USASalgado Abner J., University of Tennessee, USA2024-12-26T15:19:34Z2024-12-26T15:19:34Z2019Borthagaray, J, Nochetto, R y Salgado, A. Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. Mathematical Models and Methods in Applied Sciences [preprint], 2019, 29(14), 2679-2717https://hdl.handle.net/20.500.12008/47766We obtain regularity results in weighted Sobolev spaces for the solution of the obstacle problem for the integral fractional Laplacian (−Δ)s in a Lipschitz bounded domain Ω⊂Rn satisfying the exterior ball condition. The weight is a power of the distance to the boundary ∂Ω of Ω that accounts for the singular boundary behavior of the solution for any 0<s<1. These bounds then serve us as a guide in the design and analysis of a finite element scheme over graded meshes for any dimension n, which is optimal for n=2.Submitted by Ribeiro Jorge (jribeiro@fing.edu.uy) on 2024-12-18T17:48:24Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) BNS19.pdf: 1561047 bytes, checksum: 38a39ace11f8d3e1f1c1a80034eb1b7c (MD5)Approved for entry into archive by Machado Jimena (jmachado@fing.edu.uy) on 2024-12-26T15:12:10Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) BNS19.pdf: 1561047 bytes, checksum: 38a39ace11f8d3e1f1c1a80034eb1b7c (MD5)Made available in DSpace by Camps Karina (kcamps@psico.edu.uy) on 2024-12-26T15:19:34Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 13adb202270a5f7cee03e795b33133c4 (MD5) BNS19.pdf: 1561047 bytes, checksum: 38a39ace11f8d3e1f1c1a80034eb1b7c (MD5) Previous issue date: 2019Juan Pablo Borthagaray ha sido financiado en parte por la subvención DMS-1411808 de la NSF.26 p.application/pdfenengMathematical Models and Methods in Applied Sciences, 2019, 29(14), 2679-2717.Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)Obstacle problemFree boundariesFinite elementsFractional diffusionWeighted Sobolev spacesGraded meshesWeighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian.Preprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaBorthagaray, Juan PabloNochetto, Ricardo H.Salgado, Abner J.LICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/47766/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/47766/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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públicahttps://udelar.edu.uy/https://www.colibri.udelar.edu.uy/oai/requestkarina.camps@seciu.edu.uyUruguayopendoar:47712024-12-26T15:19:34COLIBRI - Universidad de la Repúblicafalse |
| spellingShingle | Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. Borthagaray, Juan Pablo Obstacle problem Free boundaries Finite elements Fractional diffusion Weighted Sobolev spaces Graded meshes |
| status_str | submittedVersion |
| title | Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. |
| title_full | Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. |
| title_fullStr | Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. |
| title_full_unstemmed | Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. |
| title_short | Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. |
| title_sort | Weighted Sobolev regularity and rate of approximation of the obstacle problem for the integral fractional Laplacian. |
| topic | Obstacle problem Free boundaries Finite elements Fractional diffusion Weighted Sobolev spaces Graded meshes |
| url | https://hdl.handle.net/20.500.12008/47766 |
