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A variational convergence for bifunctionals. Application to a model of strong junction

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  • We introduce a notion of variational convergence for bifunctionals in an abstract setting. Then we apply this convergence to the asymptotic analysis of a junction problem in order to capture the gradient oscillations in the joint by considering the energy functional as a bifunctional of Sobolev-function/Young measure arguments. The well known asymptotic model described in terms of Sobolev-functions is obtained by eliminating the Young-measure argument considered as an internal variable through a marginal map. Furthermore, the surface energy of the classical model can be considered as a relaxation of a Dirichlet condition.
    Mathematics Subject Classification: 49J45, 74N15, 35B40.


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