Pointwise polarization tensor bounds, and applications to voltage perturbations caused by thin inhomogeneities

Article type: Research Article

Authors: Capdeboscq, Yves | Vogelius, Michael S.

Affiliations: Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin-en-Yvelines, 45, avenue des États Unis, 78035 Versailles cedex, France | Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA

Abstract: The main result of this paper establishes optimal pointwise bounds for the polarization tensors that appear in representation formulae for the voltage perturbations caused by low volume fraction inhomogeneities. Furthermore it is demonstrated how these pointwise bounds may be used to derive a particularly simple version of the representation formulae in the case of thin inhomogeneities.

Journal: Asymptotic Analysis, vol. 50, no. 3-4, pp. 175-204, 2006