A Rigorous Proof of the Maxwell-Claussius-Mossotti Formula

Sun, 10/03/2013 - 10:30

We consider a large number of identical inclusions (say spherical), in a bounded domain, with conductivity different than that of the matrix. In the dilute limit, with some mild assumption on the first few marginal probability distribution (no periodicity or stationarity are assumed), we prove convergence in H1 norm of the expectation of the solution of the steady state heat equation, to the solution of an effective medium problem, which for spherical inclusions is obtained through the
Maxwell-Clausius-Mossotti formula. Error estimates are provided as well.