Closure of the set of diffusion functionals -- the one-dimensional case
type: Item
instance of: scholarly article
title: Closure of the set of diffusion functionals -- the one-dimensional case
zbMATH Open document ID: 1163.49010
published in: Potential Analysis
publication date: 2008-06-30T00:00:00Z
review text: The authors investigate the closure with respect to Mosco or \(\Gamma\)-convergence of the set of diffusion functionals in the one dimension case. In the one dimensional case it is a fact commonly accepted that any limit remains local. In article under review this fact is rigorously established. The authors consider the different notions of locality and prove that none of them are closed for the Mosco-convergence. A new definition of locality is introduced and a representation theorem for any local Dirichlet form is obtained. The representation theorem plays a crucial role for the proof of the closure theorem. It states that the closure of the set of diffusion functional coincides with the set of local Dirichlet forms.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49N10
Mathematics Subject Classification ID: 28A05
zbMATH DE Number: 5294535
zbMATH Keywords: diffusion functional
zbMATH Keywords: Dirichlet form
zbMATH Keywords: Mosco-convergence
zbMATH Keywords: \(\Gamma\)-convergence
zbMATH Keywords: local functional
author: Jean Jacques Alibert
author: Pierre Seppecher
MaRDI profile type: Publication
full work available at URL: s11118-008-9080-x
OpenAlex ID: W2015335457
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DOI: 10.1007/S11118-008-9080-X
description: scientific article; zbMATH DE number 5294535