An Impedance Effect of a Thin Adhesive Layer in Some Boundary Value and Transmission Problems Governed by Elliptic Differential Equations

In this paper we consider a problem of two bodies bonded through a thin adhesive layer (a third material) of thickness \delta. Leeting \delta go to zero, one obtain a boundary value transmission problem set on a fixed domain. We then give new results for the study of this problem set on a fixed domain, We then give new results for the study of this problem in the framework of Hoelder spaces: an explicit representation of the solution. Necessary and sufficient conditions at the interface for its optimal regularity are obtained using the semigroups theory and the real interpolation spaces.