Title: 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.