Limits of relaxed Dirichlet problems involving a non symmetric Dirichlet form
type: Item
instance of: scholarly article
title: Limits of relaxed Dirichlet problems involving a non symmetric Dirichlet form
zbMATH Open document ID: 1030.35090
DOI: 10.1007/BF02505948
author: S. Mataloni
author: Nicoletta Tchou
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2003-10-19T00:00:00Z
review text: The purpose of this paper is to extend some homogenization results to the case of nonsymmetric Dirichlet forms; the symmetric case has been previously studied by Biroli and Tchou. More precisely, let \(X\) be a locally compact separable connected Hausdorff space, \(m\) a given Radon measure supported on \(X\). Let \((a,D[a])\) be a nonsymmetric Dirichlet form on \(L^2(X,m)\) with strongly local symmetric and antisymmetric parts. The authors also assume that the symmetric part has all the properties required by Biroli and Tchou in the symmetric case. Then, under all these assumptions, the authors show that it is possible to define the domain of the form \(D[a]\) restricted to any open subset \(A\) of \(X\). After that they prove some compactness results in order to study the asymptotic behaviour of the solutions of \[ \begin{cases} Lu_h=f& \text{in} \Omega_h,\\ u_h=0& \text{on} \;\partial \Omega_h, \end{cases} \] where the domain varies as the parameter \(h\) goes to \(0\). The case of perforated domain and the relaxed Dirichlet problem are also considered.
reviewed by: Giuseppe Di Fazio
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 1993719
zbMATH Keywords: Dirichlet form
zbMATH Keywords: relaxed Dirichlet problem
zbMATH Keywords: degenerate elliptic equations
MaRDI profile type: Publication
cites work: Q5186236
cites work: DIRICHLET SPACES
cites work: Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
cites work: A Saint-Venant type principle for Dirichlet forms on discontinuous media
cites work: Q4284716
cites work: Q4364829
cites work: Asymptotic behaviour of relaxed Dirichlet problems involving a Dirichlet-Poincaré form
cites work: Relaxation for Dirichlet problems involving a Dirichlet form
cites work: A derivation theorem for capacities with respect to a Radon measure
cites work: Q3477252
cites work: Q2548398
cites work: Q3805370
cites work: An introduction to \(\Gamma\)-convergence
cites work: Limits of variational problems for Dirichlet forms in varying domains
cites work: NEW RESULTS ON THE ASYMPTOTIC BEHAVIOR OF DIRICHLET PROBLEMS IN PERFORATED DOMAINSDIRICHLET PROBLEMS IN PERFORATED DOMAINS
cites work: Wiener criteria and energy decay for relaxed Dirichlet problems
cites work: Wiener's criterion and \(\Gamma\)-convergence
cites work: The local regularity of solutions of degenerate elliptic equations
cites work: Q4009488
cites work: A fundamental solution for a subelliptic operator
cites work: Q3855442
cites work: The Poincaré inequality for vector fields satisfying Hörmander's condition
cites work: Q3772595
cites work: Mesures associées à une forme de Dirichlet. Applications
cites work: The sharp Poincaré inequality for free vector fields: An endpoint result
cites work: Introduction to the theory of (non-symmetric) Dirichlet forms
cites work: Representation formulas for non-symmetric Dirichlet forms
cites work: Q4944456
cites work: Composite media and asymptotic Dirichlet forms
cites work: Q3974090
cites work: Q5737280
cites work: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
description: scientific article; zbMATH DE number 1993719