Uniform Bounds on the Gradients in Composite Media Containing Close-to-Touching Inclusions: An integral Equation Approach

Eric Bonnetier (1)

1 EDP - Equations aux Dérivées Partielles

We discuss point wise bounds on the gradient of the solution to a scalar elliptic PDE in a 2D composite media containing smooth inclusions as the inter-inclusion distance tends to 0. THe solution is expressed in terms of layer potentials and we study the uniform invertibility of the associated system. We also show that, when the inclusions are disks, the spectrum of the Neumann-Poincaré operator appearing in the integral equations relates to the bounds on the gradients.

Domaines: Equations aux dérivées partielles [math.AP]

Eric Bonnetier. Uniform Bounds on the Gradients in Composite Media Containing Close-to-Touching Inclusions: An integral Equation Approach. ICIPA 2012 - International Conference on Inverse Problems and Applications in Honor of Gunther Uhlmann's 60th Birthday, Sep 2012, Hangzhou, China. ⟨hal-00750497⟩