Closure of the Set of Diffusion Functionals - the One Dimensional Case

Jean-Jacques Alibert (1) , Pierre Seppecher (2)

1 ANLA - Laboratoire d'Analyse Non Linéaire Appliquée
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

We characterize the closure with respect to Mosco or Gamma-convergence of the set of diffusion functionals in the one dimension case. As commonly accepted we find this closure is a set of local Dirichlet forms. The difficulty is to identify the right notion of locality. We compare different possible definitions. We give a representation theorem for the elements of the considered closure.

Mots clés: Homogenization; Mosco-convergence; Gamma-convergence; Local functionals; Dirichlet forms

Domaines: Analyse fonctionnelle [math.FA]

Jean-Jacques Alibert, Pierre Seppecher. Closure of the Set of Diffusion Functionals - the One Dimensional Case. Potential Analysis, 2008, 28 (4), pp.335-356. ⟨hal-00527074⟩