Fibered microstructures for some nonlocal Dirichlet forms

Marc Briane ^[1] ; Nicoletta Tchou ^[2]
1. [1] I.N.S.A. & I.R.M.A.R., France
2. [2] Université de Rennes I, France
Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 30, Nº 3-4, 2001, págs. 681-711
Idioma: inglés
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Resumen
- In this article we study the homogenization of some fibered microstructures in order to obtain prescribed nonlocal effects from strongly local conduction problems in a bounded open set S2 of R . According to the Beurling-Deny formula these nonlocal effects are represented by a so-called jumping measure defined on the product Q x Q. In particular we reach the measures of type j (dx, dy) = IE (dy) where E is a smooth open subset of Q. If the set E is connected the starting microstructure is only composed of high conductivity fibers. If the set E is not connected we also need a mixture of high and low conductivity fibers in the regions separating the components of E.