Closure of the set of diffusion functionals with respect to the Mosco-convergence
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چکیده
We characterize the functionals which are Mosco-limits, in the L2(Ω) topology, of some sequence of functionals of the kind Fn(u) := ∫ Ω αn(x)|∇u(x)| dx , where Ω is a bounded domain of RN (N ≥ 3). It is known that this family of functionals is included in the closed set of Dirichlet forms. Here, we prove that the set of Dirichlet forms is actually the closure of the set of diffusion functionals. A crucial step is the explicit construction of a composite material whose effective energy contains a very simple non-local interaction. keywords : Homogenization, Mosco-convergence, Γ-convergence, Dirichlet forms, composite materials.
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