Averaging of dilute random media: a rigorous proof of the Clausius-Mossotti formula
type: Item
instance of: scholarly article
title: Averaging of dilute random media: a rigorous proof of the Clausius-Mossotti formula
zbMATH Open document ID: 1277.78027
published in: Archive for Rational Mechanics and Analysis
publication date: 2013-03-27T00:00:00Z
review text: An \(H^1\)-error estimate between the physical fields \(\phi_\varepsilon\) and an average one is established via the derivations of estimates for solutions of the one- and two-particle problems. For each \(\varepsilon>0\), which represents the radius of a finite number of spherical particles of conductivity \(\sigma\) immersed into a medium of conductivity 1, \(\phi_\varepsilon\) is the unique weak solution to a Dirichlet problem: \(\nabla\cdot(a_\varepsilon\nabla\phi)=0\) in a bounded domain \(\Omega\subset\mathbb{R}^3\) of class \(C^{2,\alpha}\), for some \(\alpha>0\), with the input data belonging to \(C^{2,\alpha}(\partial\Omega)\). Here, the coefficient \(a_\varepsilon\) is given by the Clausius-Mossotti approximation. The proof is based on the potential theory.
reviewed by: Luisa Consiglieri
Mathematics Subject Classification ID: 78A48
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 6148983
zbMATH Keywords: random media
zbMATH Keywords: Clausius-Mossotti
zbMATH Keywords: potential theory
author: Y. Almog
MaRDI profile type: Publication
full work available at URL: s00205-012-0581-9
OpenAlex ID: W2088424242
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DOI: 10.1007/S00205-012-0581-9
description: scientific article; zbMATH DE number 6148983