Asymptotics in the presence of inclusions of small volume for a conduction equation: A case with a non-smooth reference potential

Eric Bonnetier (1) , Faouzi Triki (1)

1 EDP - Equations aux Dérivées Partielles

We derive an asymptotic formula for the Green function of a conduction equation in the presence of a small inhomogeneity, that perturbs a background conductivity, which is piecewise constant on an angular sector. We show how the elliptic corner singularity of the background potential affects the form of the first order term in the expansion.

Mots clés: Asymptotic expansions; small inclusion; non-smooth potential

Domaines: Equations aux dérivées partielles [math.AP]

Eric Bonnetier, Faouzi Triki. Asymptotics in the presence of inclusions of small volume for a conduction equation: A case with a non-smooth reference potential. Conference on Imaging Microstructures: Mathematical and Computational Challenges, Jun 2008, Paris, France. pp.95-112. ⟨hal-00388018⟩