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The best approximation of a given function in L2-norm by Lipschitz functions with gradient constraint

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dc.contributor.authorBuccheri, Stefano
dc.contributor.authorLeonori, Tommaso
dc.contributor.authorRossi, Julio D.
dc.contributor.orcidhttps://orcid.org/0000-0002-0667-233X
dc.contributor.orcidhttps://orcid.org/0000-0002-0848-4463
dc.contributor.orcidhttps://orcid.org/0000-0002-5905-4412
dc.date.accessioned2024-11-08T11:00:57Z
dc.date.available2024-11-08T11:00:57Z
dc.date.issued2024-04-24
dc.description.abstractThe starting point of this paper is the study of the asymptotic behavior, as p → ∞, of the following minimization problem: min{1 p ∫ Ω |∇v|p + 1 2 ∫ (v − f)2, v ∈ W1,p(Ω)}. Ω We show that the limit problem provides the best approximation, in the L2-norm, of the datum f among all Lipschitz functions with Lipschitz constant less or equal than one. Moreover, such an approximation verifies a suitable PDE in the viscosity sense. After the analysis of the model problem above, we consider the asymptotic behavior of a related family of nonvariational equations and, finally, we also deal with some functionals involving the (N − 1)-Hausdorff measure of the jump set of the function.en
dc.description.versionversión publicada
dc.identifier.citationBuccheri, Stefano, Leonori, Tommaso and Rossi, Julio D.. "The best approximation of a given function in L 2-norm by Lipschitz functions with gradient constraint" Advances in Calculus of Variations, 2024. https://doi.org/10.1515/acv-2023-0058
dc.identifier.doihttps://doi.org/10.1515/acv-2023-0058
dc.identifier.issn1864-8266
dc.identifier.urihttps://hdl.handle.net/20.500.14468/24318
dc.journal.titleAdvances in Calculus of Variations
dc.language.isoen
dc.publisherDe Gruyter
dc.relation.centerFacultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsp-Laplacianen
dc.subject.keywordsinfinity-Laplacianen
dc.subject.keywordsLipschitz approximationsen
dc.titleThe best approximation of a given function in L2-norm by Lipschitz functions with gradient constrainten
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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