dc.contributor.author
Audrito, A.
dc.contributor.author
Felipe-Navarro, J.-C.
dc.contributor.author
Ros-Oton, X.
dc.date.accessioned
2023-08-29T11:21:14Z
dc.date.accessioned
2024-09-19T14:35:32Z
dc.date.available
2023-08-29T11:21:14Z
dc.date.available
2024-09-19T14:35:32Z
dc.date.issued
2023-06-26
dc.identifier.uri
http://hdl.handle.net/2072/536866
dc.description.abstract
We study the regularity up to the boundary of solutions to the Neumann problem for the fractional Laplacian. We prove that if u is a weak solution of (Formula Presented) up to the boundary for some α > 0. Moreover, in case s > 12, we show that (Formula Presented). To prove these results we need, among other things, a delicate Moser iteration on the boundary with some logarithmic corrections. Our methods allow us to treat as well the Neumann problem for the regional fractional Laplacian, and we establish the same boundary regularity result. Prior to our results, the interior regularity for these Neumann problems was well understood, but near the boundary even the continuity of solutions was open. © 2023 Scuola Normale Superiore. All rights reserved.
eng
dc.description.sponsorship
Funding text 1: X. Ros-Oton was supported by the European Research Council (ERC) under the Grant Agreement No. 801867, by the AEI project PID2021-125021NAI00 (Spain), by the AGAUR Grant 2021 SGR 00087 (Catalunya), and by the AEI Maria de Maeztu Program for Centers and Units of Excellence in R&D CEX2020-001084-M. A. Audrito and X. Ros-Oton were supported by the Swiss National Science Foundation (SNF). J. C. Felipe-Navarro and X. Ros-Oton were supported by the MINECO Grant RED2022-134784-T (Spain). J. C. Felipe-Navarro acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO), through the Maria de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445-16-4). Part of this work has been done while J. C. Felipe-Navarro was visiting Universität Zürich.; Funding text 2: X. Ros-Oton was supported by the European Research Council (ERC) under the Grant Agreement No. 801867, by the AEI project PID2021-125021NAI00 (Spain), by the AGAUR Grant 2021 SGR 00087 (Catalunya), and by the AEI Maria de Maeztu Program for Centers and Units of Excellence in R&D CEX2020-001084-M. A. Audrito and X. Ros-Oton were supported by the Swiss National Science Foundation (SNF). J. C. Felipe-Navarro and X. Ros-Oton were supported by the MINECO Grant RED2022-134784-T (Spain). J. C. Felipe-Navarro acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO), through the Maria de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445-16-4). Part of this work has been done while J. C. Felipe-Navarro was visiting Universität Zürich. Received May 10, 2021; accepted in revised form February 1, 2022. Published online June 2023.
dc.format.extent
55 p.
cat
dc.publisher
Scuola Normale Superiore
cat
dc.relation.ispartof
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
cat
dc.rights
This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). https://rightsstatements.org/page/InC/1.0/?language=en
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Neumann problem, boundary regularity, fractional Laplacian
cat
dc.title
The Neumann problem for the fractional Laplacian: regularity up to the boundary
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/acceptedVersion
cat
dc.identifier.doi
10.2422/2036-2145.202105_096
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
