Pointwise bounds on the gradients in a composite medium and the Neumann-Poincaré operator

Eric Bonnetier (1) , Faouzi Triki (1)

1 EDP - Equations aux Dérivées Partielles

In composite media containing close-to-touching inhomogeneities, the gradients of the voltage potential may become unbounded in the narrow channels between the inclusions, as the inter-inclusion distance tends to 0, and as the contrast of material coefficients becomes large. When the inclusions are discs in 2D, we show that the point wise regularity properties of the gradients can be inferred from the study of the spectral properties of the Neumann-Poincaré operator. This operator appears in the integral formulation of the transmission problem.

Domaines: Equations aux dérivées partielles [math.AP]

Eric Bonnetier, Faouzi Triki. Pointwise bounds on the gradients in a composite medium and the Neumann-Poincaré operator. French-Mexican Meeting on Industrial and Applied Mathematics, Nov 2013, Villa Hermosa, Mexico. ⟨hal-00987286⟩