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 $. Leting $\delta $ go to zero, one obtains a boundary value transmission problem set on a fixed domain. We then give new results for the study of this problem in the framework of Hölder spaces: an explicit representation of the solution and necessary and sufficient conditions at the interface for its optimal regularity are obtained using the semigroups theory and the real interpolation spaces.