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dc.contributor.authorAwi, Romeo
dc.contributor.authorSedjro, Marc
dc.date.accessioned2017-12-28T07:32:15Z
dc.date.available2017-12-28T07:32:15Z
dc.date.issued2017-02-05
dc.identifier.urihttp://hdl.handle.net/10754/626531
dc.description.abstractWe prove existence and uniqueness of minimizers for a family of energy functionals that arises in Elasticity and involves polyconvex integrands over a certain subset of displacement maps. This work extends previous results by Awi and Gangbo to a larger class of integrands. First, we study these variational problems over displacements for which the determinant is positive. Second, we consider a limit case in which the functionals are degenerate. In that case, the set of admissible displacements reduces to that of incompressible displacements which are measure preserving maps. Finally, we establish that the minimizer over the set of incompressible maps may be obtained as a limit of minimizers corresponding to a sequence of minimization problems over general displacements provided we have enough regularity on the dual problems. We point out that these results defy the direct methods of the calculus of variations.
dc.publisherarXiv
dc.relation.urlhttp://arxiv.org/abs/1702.01471v1
dc.relation.urlhttp://arxiv.org/pdf/1702.01471v1
dc.rightsArchived with thanks to arXiv
dc.titleOn the uniqueness of minimizers for a class of variational problems with Polyconvex integrand
dc.typePreprint
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.eprint.versionPre-print
dc.contributor.institutionInstitute for Mathematics and its Applications, 207 Church Street, Minneapolis, MN 55455
dc.identifier.arxividarXiv:1702.01471
kaust.personSedjro, Marc
refterms.dateFOA2018-06-13T12:20:29Z


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