The Clausius--Mossotti Formula in a Dilute Random Medium with Fixed Volume Fraction
Yaniv Almog · Multiscale Modeling and Simulation · 2014
We consider a medium composed of randomly dispersed spherical, identical inclusions in a bounded domain, with conductivity different than that of the host medium. We study the limit where the number inclusions tends to infinity but their volume fraction remains fixed. For small volume fractions, we prove convergence, in the $W^{1,p}$ norm ($1