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On problems in the calculus of variations in increasingly elongated domains

Abstract

We consider minimization problems in the calculus of variations set in a sequence of domains the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain constant. We study the asymptotic behavior of minimizers in various situations and show that they converge in an appropriate sense toward minimizers of a related energy functional in the constant directions.
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Dates and versions

hal-01517824 , version 1 (03-05-2017)
hal-01517824 , version 2 (19-06-2017)
hal-01517824 , version 3 (18-01-2018)

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Hervé Le Dret, Amira Mokrane. On problems in the calculus of variations in increasingly elongated domains. 2017. ⟨hal-01517824v1⟩
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