On the spectrum of the Poincaré variational problem for two close-to-touching inclusions in 2D

Eric Bonnetier (1) , Faouzi Triki (1)

1 EDP - Equations aux Dérivées Partielles

We study the spectrum of the Poincaré variational problem for two close to touching inclusions in R^2. We derive the asymptotics of its eigenvalues as the distance between the inclusions tends to zero.

Domaines: Equations aux dérivées partielles [math.AP]

Eric Bonnetier, Faouzi Triki. On the spectrum of the Poincaré variational problem for two close-to-touching inclusions in 2D. Archive for Rational Mechanics and Analysis, 2013, 209 (2), pp.541-567. ⟨10.1007/s00205-013-0636-6⟩. ⟨hal-00997208⟩