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Oscillating minimizers of a fourth order problem invariant under scaling

dc.contributor.authorCatto, Isabelle
HAL ID: 742722
ORCID: 0000-0002-5463-2340
dc.contributor.authorDolbeault, Jean
HAL ID: 87
ORCID: 0000-0003-4234-2298
dc.contributor.authorBenguria, Rafael
dc.contributor.authorMonneau, Régis
dc.date.accessioned2009-07-02T17:06:00Z
dc.date.available2009-07-02T17:06:00Z
dc.date.issued2004
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/697
dc.language.isoenen
dc.subjectFourth-order operators
dc.subjectLoss of compactness
dc.subjectInequalities
dc.subjectMinimizationen
dc.subjectScaling invariance
dc.subjectEuler–Lagrange equation
dc.subjectLagrange multiplier
dc.subjectShooting method
dc.subjectCommutator method for Lieb– Thirring inequalities
dc.subjectLieb–Thirring inequalities
dc.subject.ddc515en
dc.titleOscillating minimizers of a fourth order problem invariant under scalingen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherINRIA - Ecole Nationale des Ponts et Chaussées;
dc.contributor.editoruniversityotherPontifica Universidad Catolica de Chile;Chili
dc.description.abstractenBy variational methods, we prove the inequality $$\int_\R u''{}^2\,dx-\int_\R u''\,u^2\,dx\geq I\,\int_\R u^4\,dx\quad \forall\; u\in L^4(\R)\;\mbox{such that}\; u''\in L^2(\R) $$ for some constant $I\in (-9/64,-1/4)$. This inequality is connected to Lieb-Thirring type problems and has interesting scaling properties. The best constant is achieved by sign changing minimizers of a problem on periodic functions, but does not depend on the period. Moreover, we completely characterize the minimizers of the periodic problem.en
dc.relation.isversionofjnlnameJournal of Differential Equations
dc.relation.isversionofjnlvol205en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2004
dc.relation.isversionofjnlpages253-269en
dc.relation.isversionofdoihttp://dx.doi.org/10.1016/j.jde.2004.03.024en
dc.description.sponsorshipprivateouien
dc.subject.ddclabelAnalyseen


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