Closure of the set of diffusion functionals with respect to the mosco-convergence

We characterize the functionals which are Mosco-limits, in the L-2(Q) topology, of some sequence of functionals of the kind F-n(u) := integral(Omega) alpha(n)(x)\delu(x)\(2) dx, where Q is a bounded domain of R-N(N greater than or equal to 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 nonlocal interaction.