Regularity for a class of degenerate fully nonlinear nonlocal elliptic equations

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dc.contributor.authorFang, Yuzhoucs
dc.contributor.authorRadulescu, Vicentiucs
dc.contributor.authorZhang, Chaocs
dc.coverage.issue5cs
dc.coverage.volume64cs
dc.date.accessioned2025-07-17T07:59:35Z
dc.date.available2025-07-17T07:59:35Z
dc.date.issued2025-06-06cs
dc.description.abstractWe consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of viscosity solutions according to different diffusion orders. More precisely, when the order of the fractional diffusion is sufficiently close to 2, we obtain Hölder continuity for the gradient of any viscosity solutions and further derive an improved gradient regularity estimate at the origin. For the order of the fractional diffusion in the interval (1, 2), we prove that there is at least one solution of class Cloc1,. Additionally, if the order of the fractional diffusion is in the interval (0, 1], the local Hölder continuity of solutions is inferred.en
dc.formattextcs
dc.format.extent1-29cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationCALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. 2025, vol. 64, issue 5, p. 1-29.en
dc.identifier.doi10.1007/s00526-025-03023-4cs
dc.identifier.issn0944-2669cs
dc.identifier.orcid0000-0003-4615-5537cs
dc.identifier.other198077cs
dc.identifier.researcheridA-1503-2012cs
dc.identifier.scopus35608668800cs
dc.identifier.urihttps://hdl.handle.net/11012/255174
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofCALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONScs
dc.relation.urihttps://link.springer.com/article/10.1007/s00526-025-03023-4cs
dc.rightsCreative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0944-2669/cs
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/cs
dc.subjectintegrodifferential equationsen
dc.subjectviscosity solutionsen
dc.subjectmaximum principleen
dc.subjectholder continuityen
dc.subjectinterioren
dc.titleRegularity for a class of degenerate fully nonlinear nonlocal elliptic equationsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-198077en
sync.item.dbtypeVAVen
sync.item.insts2025.07.17 09:59:35en
sync.item.modts2025.07.17 09:33:49en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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