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\(\Gamma\)-convergence of functionals on divergence-free fields. (English) Zbl 1127.49011

The authors study the stability of a sequence of integral functionals on divergence free matrix-valued functions using the method of \(\Gamma\)-convergence. They prove that the \(\Gamma\)-limit of the sequence is again a functional of the same type. The \(\Gamma\)-limit is also stable under volume constraints and various type of boundary conditions.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
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