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Strong convergence of the gradients for p-Laplacian problems as p → ∞

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dc.contributor.authorBuccheri, Stefano
dc.contributor.authorLeonori, Tommaso
dc.contributor.authorRossi, Julio D.
dc.date.accessioned2024-11-19T12:53:37Z
dc.date.available2024-11-19T12:53:37Z
dc.date.issued2021-03-01
dc.description.abstractIn this paper we prove that the gradients of solutions to the Dirichlet problem for −∆pup = f , with f > 0, converge as p → ∞ strongly in every Lq with 1 ≤ q < ∞ to the gradient of the limit function. This convergence is sharp since a simple example in 1-d shows that there is no convergence in L∞. For a nonnegative f we obtain the same strong convergence inside the support of f . The same kind of result also holds true for the eigenvalue problem for a suitable class of domains (as balls or stadiums).en
dc.description.versionversión final
dc.identifier.citationStefano Buccheri, Tommaso Leonori, Julio D. Rossi, Strong convergence of the gradients for p-Laplacian problems as p → ∞, Journal of Mathematical Analysis and Applications, Volume 495, Issue 1, 2021, 124724, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2020.124724.
dc.identifier.doihttps://doi.org/10.1016/j.jmaa.2020.124724
dc.identifier.issn0022-247X
dc.identifier.urihttps://hdl.handle.net/20.500.14468/24426
dc.journal.issue1
dc.journal.titleJournal of Mathematical Analysis and Applications
dc.journal.volume495
dc.language.isoen
dc.publisherElsevier
dc.relation.centerFacultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.titleStrong convergence of the gradients for p-Laplacian problems as p → ∞es
dc.typejournal articleen
dspace.entity.typePublication
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