Geodesic
An impedance effect of a thin adhesive layer in some boundary value and transmission problems governed by elliptic differential equations
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 4, pp. 50-75

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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.
Keywords: boundary value problem of elliptic type; transmission problems; impedance effect; thin layer. 
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     title = {An impedance effect of a thin adhesive layer in some boundary value and transmission problems governed by elliptic differential equations},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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A. Favini; R. Labbas; K. Lemrabet. An impedance effect of a thin adhesive layer in some boundary value and transmission problems governed by elliptic differential equations. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 4, pp. 50-75. http://geodesic.mathdoc.fr/item/VYURU_2015_8_4_a4/