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dc.creatorBriane, Marces
dc.creatorCasado Díaz, Juanes
dc.date.accessioned2016-09-27T08:04:14Z
dc.date.available2016-09-27T08:04:14Z
dc.date.issued2016-04-05
dc.identifier.citationBriane, M. y Casado Díaz, J. (2016). A new div-curl result. Applications to the homogenization of elliptic systems and to the weak continuity of the Jacobian. Journal of Differential Equations, 260 (7), 5678-5725.
dc.identifier.issn0022-0396es
dc.identifier.urihttp://hdl.handle.net/11441/45733
dc.description.abstractIn this paper a new div-curl result is established in an open set Ω of R N , N ≥ 2, for the product of two sequences of vector-valued functions which are bounded respectively in Lp (Ω)N and Lq (Ω)N , with 1/p + 1/q = 1 + 1/(N − 1), and whose respectively divergence and curl are compact in suitable spaces. We also assume that the product converges weakly in W−1,1 (Ω). The key ingredient of the proof is a compactness result for bounded sequences in W1,q(Ω), based on the imbedding of W1,q(SN−1) into Lp ′ (SN−1) (SN−1 the unit sphere of R N ) through a suitable selection of annuli on which the gradients are not too high, in the spirit of [26, 32]. The div-curl result is applied to the homogenization of equi-coercive systems whose coefficients are equi-bounded in Lρ (Ω) for some ρ > N−1 2 if N > 2, or in L1 (Ω) if N = 2. It also allows us to prove a weak continuity result for the Jacobian for bounded sequences in W1,N−1 (Ω) satisfying an alternative assumption to the L∞-strong estimate of H. Brezis & H. Nguyen: “The Jacobian determinant revisited”, Invent. Math., 185 (1) (2011), 17-54. Two examples show the sharpness of the results.es
dc.description.sponsorshipMinisterio de Economía y Competitividades
dc.description.sponsorshipInstitut de Recherche Mathématique de Renneses
dc.formatapplication/pdfes
dc.language.isoenges
dc.publisherElsevieres
dc.relation.ispartofJournal of Differential Equations, 260 (7), 5678-5725.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectDiv-curles
dc.subjectHomogenizationes
dc.subjectElliptic systemses
dc.subjectNon equi-bounded coefficientses
dc.subjectΓ-convergencees
dc.subjectH-convergencees
dc.subjectJacobianes
dc.subjectWeak continuityes
dc.titleA new div-curl result. Applications to the homogenization of elliptic systems and to the weak continuity of the Jacobianes
dc.typeinfo:eu-repo/semantics/articlees
dcterms.identifierhttps://ror.org/03yxnpp24
dc.type.versioninfo:eu-repo/semantics/submittedVersiones
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.contributor.affiliationUniversidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numéricoes
dc.relation.projectIDinfo:eu-repo/grantAgreement/MINECO/MTM2014-53309-Pes
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.jde.2015.12.029es
dc.identifier.doi10.1016/j.jde.2015.12.029es
dc.contributor.groupUniversidad de Sevilla. FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parcialeses
idus.format.extent40 p.es
dc.journaltitleJournal of Differential Equationses
dc.publication.volumen260es
dc.publication.issue7es
dc.publication.initialPage5678es
dc.publication.endPage5725es
dc.identifier.idushttps://idus.us.es/xmlui/handle/11441/45733
dc.contributor.funderMinisterio de Economía y Competitividad (MINECO). España
dc.contributor.funderInstitut de Recherche Mathématique de Rennes

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