Homogenization of a transmission problem with sign-changing coefficients and interfacial flux jump

Abstract

We study the homogenization of a scalar problem posed in a composite medium made up of two materials, a positive and a negative one. An important feature is the presence of a flux jump across their oscillating interface. The main difficulties of this study are due to the sign-changing coefficients and the appearance of an unsigned surface integral term in the variational formulation. A proof by contradiction (nonstandard in this context) and T‑coercivity technics are used in order to cope with these difficulties.