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Composite media and Dirichlet forms

  • Umberto Mosco
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 5)

Abstract

Some relevant “macroscopic” features of bodies with complicated “microscopic” structure are usually described, in the mathematical theory of composite media and homogenization, in terms of asymptotic properties of sequences of Dirichlet integrals
$$ {E_h} = \mathop{\smallint }\limits_{\Omega } \sum\limits_{{ij = 1}}^N {{\partial_i}u} {\partial_j}u \,a_h^{{ij}}(x)dx\;,h \in \mathbb{N}, $$
(1)
\( {\partial_i} = {{{\partial u}} \left/ {{\partial xi,{\partial_j} }} \right.} = {{{\partial u}} \left/ {{\partial xj}} \right.} \), by appropriately defining the “conductivity” coefficients \( a_h^{{ij}}(x) \) on some open subset Ω of ℝN.

Keywords

Radon Measure Dirichlet Form Selfadjoint Operator Symmetric Bilinear Form Resolvent Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    J.R. Baxter, G. Dal Maso, U. Mosco, Stopping times and Γ-convergerne, Trans. AMS 303 (1987), 1–38.MATHGoogle Scholar
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    R. Gulliver, G. Dal Maso, U. Mosco, Asymptotic spectrum of manifolds of increasing topological type, Universität Bonn SFB 256 Preprint Series, to appear.Google Scholar
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    G. Dal Maso, U. Mosco, Wiener’s criterion and Γ-convergence, J. Appl. Math. and Opt 15 (1987), 15–63.MATHCrossRefGoogle Scholar
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    U. Mosco, Composite media and asymptotic Dirichlet forms, to appear.Google Scholar
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    U. Mosco, Compact families of Dirichlet forms, to appear.Google Scholar

Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Umberto Mosco
    • 1
  1. 1.Dipartimento di MatematicaUniversità “La Sapienza”RomaItaly

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