Existence and homogenization for a singular problem through rough surfaces

The paper deals with existence and homogenization for elliptic problems with lower order terms singular in the u-variable (u is the solution) in a cylinder Q in R^N, so that the lower order term becomes infinite on the set u = 0. A rapidly oscillating interface inside Q separates the cylinder in two composite connected components. The interface has a periodic microstructure and it is situated in a small neighbourhood of a hyperplane which separates the two components of Q. At the interface we suppose the following transmission conditions: (i) the flux is continuous, (ii) the jump of a solution at the interface is proportional to the flux through the interface. This is a steady state model for the heat conduction in two heterogeneous electrically conducting materials with an imperfect contact between them. On the exterior boundary Dirichlet boundary conditions are prescribed.We also derive a corrector result for every values of the two parameters which are related respectively to the microstructure period and to the amplitude of the interface oscillations.