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

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

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