Pointwise Estimates on the Gradients in a Medium Containing Close to Touching Inclusions: an Integral Equation Approach
Résumé
We consider an elliptic equation for a 2D composite medium that contains conducting inclusions with C1,α boundaries. When the inclusions are separated by a distance δ>0, the solution can be represented by layer potentials. We study the asymptotic limit as δ→0 of the associated system of integral equations. In the particular case of discs, we show how the spectral properties of the system of integral equations relates to the behavior of the potential around the contact zone.