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Publication 98-CNA-00u
On a Volume Constrained Variational Problem Luigi Ambrosio, Irene Fonseca, Paolo Marcellini, and Luc Tartar Abstract: Existence of minimizers for a volume constrained energy where is proved for the case in which are extremal points of a compact, convex set in and under suitable assumptions on a class of quasiconvex energy densities W. Optimality properties are studied in the scalar-valued problem where d=1, P=2, , and the -limit as the sum of the measures of the 2 phases tends to is identified. Minimizers are fully characterized when N=1, and candidates for solutions are studied for the circle and the square in the plane.
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