Derivation of macroscopic equilibrium models for heat conduction in finely mixed composite media with singular sources

We prove existence and homogenization results for a family (depending on a small parameter and on a parameter 2 f1; 0; 1g) of elliptic problems involving a singular lower order term and representing the Euler equations of energy functionals, which can be used to describe the equilibrium for the heat conduction in composite materials with two finely mixed phases having a microscopic periodic structure (for details on the related physical models see for instance [3, 4] and the reference quoted there). The same kind of energies can be also useful to study the electrical conduction in biological tissues (see for instance [1, 2], where the related parabolic problems without singular source are studied).