On a volume constrained variational problem

Luigi Ambrosio, Irene Fonseca, Paolo Marcellini, and Luc Tartar

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Submission date: 21. Jul. 1998
Pages: 23
published in: Archive for rational mechanics and analysis, 149 (1999) 1, p. 23-47 
DOI number (of the published article): 10.1007/s002050050166
Bibtex
MSC-Numbers: 35A15, 35J65, 49J45, 49K20
Keywords and phrases: volume constraints, free boundary problems
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Abstract:
Existence of minimizers for a volume constrained energy

where is proved in the case where 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.