A Saint-Venant type principle for Dirichlet forms on discontinuous media
type: Item
instance of: scholarly article
title: A Saint-Venant type principle for Dirichlet forms on discontinuous media
zbMATH Open document ID: 0851.31008
DOI: 10.1007/BF01759352
author: Umberto Mosco
author: Marco Biroli
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1996-05-14T00:00:00Z
review text: The authors of this very interesting paper consider families of Dirichlet forms of diffusion type which describe the variational behavior of possibly highly non-homogeneous and non-isotropic bodies. Structural Harnack inequality and Saint-Venant type energy decays are proved for their local solutions. Estimates for the Green functions are also derived. From the point of view of partial differential equations the theory elaborated in the paper finds its main motivation in the study of structural properties of second order degenerate elliptic operators. New important results, such as Harnack's inequality, estimates for the Green function and bounds for energy decay, are obtained for weighted uniformly elliptic operators in divergence form with measurable coefficients, as well as for uniformly subelliptic (selfadjoint) second order operators with bounded measurable coefficients.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 31B35
Mathematics Subject Classification ID: 74E05
zbMATH DE Number: 878428
zbMATH Keywords: Saint-Venant principle
zbMATH Keywords: Dirichlet forms of diffusion type
zbMATH Keywords: Harnack inequality
zbMATH Keywords: Green functions
zbMATH Keywords: second order degenerate elliptic operators
zbMATH Keywords: energy decay
zbMATH Keywords: measurable coefficients
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01759352
OpenAlex ID: W2091846918
description: scientific article; zbMATH DE number 878428