Singular Functions and Characterizations of Field Concentrations: A Survey

Abstract

In the presence of closely located inclusions of the extreme material property, the physical fields, such as the electric field and the stress tensor, may be concentrated and arbitrarily large in the narrow region between two inclusions. Recently there has been significant progress on the quantitative characterization of the field concentration in the contexts of electrostatics (Laplace equation), linear elasticity (Lamé system), and viscous flow (Stokes system). This paper is to review such progress in a coherent way.