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Approximation of variational problems with a convexity constraint by PDEs of Abreu type

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorCarlier, Guillaume
hal.structure.identifierDipartimento di Matematica e Applicazioni “Renato Caccioppoli”
dc.contributor.authorRadice, Teresa
dc.date.accessioned2019-02-20T16:31:26Z
dc.date.available2019-02-20T16:31:26Z
dc.date.issued2019
dc.identifier.issn0944-2669
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18467
dc.language.isoenen
dc.subjectAbreu equation
dc.subjectMonge-Ampère operator
dc.subjectcalculus of varia-
dc.subjecttions with a convexity constraint
dc.subject.ddc515en
dc.titleApproximation of variational problems with a convexity constraint by PDEs of Abreu type
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenMotivated by some variational problems subject to a convexity constraint, we consider an approximation using the logarithm of the Hessian determinant as a barrier for the constraint. We show that the minimizer of this penalization can be approached by solving a second boundary value problem for Abreu's equation which is a well-posed nonlinear fourth-order elliptic problem. More interestingly, a similar approximation result holds for the initial constrained variational problem.
dc.relation.isversionofjnlnameCalculus of Variations and Partial Differential Equations
dc.relation.isversionofjnlvol58
dc.relation.isversionofjnldate2019
dc.relation.isversionofjnlpages16
dc.relation.isversionofdoi10.1007/s00526-019-1613-1
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-02-22T10:41:02Z
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