CLOSURE OF THE SET OF DIFFUSION FUNCTIONALS WITH RESPECT TO THE MOSCO-CONVERGENCE
Mohamed Camar-Eddine, Pierre Seppecher · Mathematical Models and Methods in Applied Sciences · 2002
We characterize the functionals which are Mosco-limits, in the L2(Ω) topology, of some sequence of functionals of the kind [Formula: see text] 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 nonlocal interaction.