dc.contributor.author
Csato, Gyula
dc.contributor.author
Mas Blesa, Albert
dc.date.accessioned
2025-06-16T07:29:00Z
dc.date.available
2025-06-16T07:29:00Z
dc.date.issued
2025-06-01
dc.identifier.uri
http://hdl.handle.net/2072/484442
dc.description.abstract
We discuss the Hölder regularity of solutions to the semilinear equation involving the fractional Laplacian (−Δ)su=f(u) in one dimension. We put in evidence a new regularity phenomenon which is a combined effect of the nonlocality and the semilinearity of the equation, since it does not happen neither for local semilinear equations, nor for nonlocal linear equations. Namely, for nonlinearities f in Cβ and when 2s+β<1, the solution is not always C2s+β−ϵ for all ϵ>0. Instead, in general the solution u is at most C2s/(1−β).
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dc.description.sponsorship
The two authors are supported by the Spanish grants PID2021-123903NB-I00 and RED2022-134784-T funded by MCIN/AEI/10.13039/501100011033 and by ERDF \u201CA way of making Europe\u201D, and by the Catalan grant 2021-SGR-00087 . The first author is in addition supported by the Spanish grant PID2021-125021NA-I00 . This work is supported by the Spanish State Research Agency , through the Severo Ochoa and Mar\u00EDa de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M)
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dc.format.extent
13 p.
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dc.relation.ispartof
Nonlinear Analysis, Theory, Methods and Applications
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dc.rights
Attribution 4.0 International
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Fractional Laplacian
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dc.subject.other
Hölder regularity
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dc.subject.other
Semilinear equations
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dc.title
Examples of optimal Hölder regularity in semilinear equations involving the fractional Laplacian
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dc.type
info:eu-repo/semantics/article
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dc.description.version
info:eu-repo/semantics/publishedVersion
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dc.identifier.doi
10.1016/j.na.2025.113755
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dc.rights.accessLevel
info:eu-repo/semantics/openAccess
