On a Volume Constrained Variational
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چکیده
Existence of minimizers for a volume constrained energy E(u) := Z W (ru) dx where L N (fu = zig) = i; i = 1; : : : ; P; is proved in the case where zi are extremal points of a compact, convex set in R d 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, W () = jj 2 , and the ?-limit as the sum of the measures of the 2 phases tends to L N (() is identiied. 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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تاریخ انتشار 1998