Bounds on the eigenvalues of the Neumann-Poincaré operator for 2 close-to-touching $C^{m+1}$ inclusions

Eric Bonnetier (1) , Faouzi Triki (1)

1 EDP - Equations aux Dérivées Partielles

We study the spectrum of the Neumann-Poincaré operator for 2 close-to-touching conducting inclusions in 2D. We derive the asymptotic behavior of its eigenvalues when the inter-inclusion distance tends to 0, in terms of the smoothness of the contact when the inclusions touch.

Mots clés: Poincaré-Neumann operator; non self-adjoint operators; asymptotic analysis

Domaines: Equations aux dérivées partielles [math.AP]

Eric Bonnetier, Faouzi Triki. Bounds on the eigenvalues of the Neumann-Poincaré operator for 2 close-to-touching $C^{m+1}$ inclusions. Coupled Physics Inverse Problems, Jan 2013, Santiago, Chile. ⟨hal-00987285⟩