Résumé:
This thesis is devoted essentially to study, in two frameworks, the existence, uniqueness
and maximal regularity of the solutions of a family of transmission problems governed by an
abstract second order di¤erential equations with Robin boundary conditions.
In the rst framework (Lp spaces), we treated two transmission problems, under certain
assumptions on the operators (ellipticity, Bip, commutativity) and on the space (UMD or
not).
In the second framework, we studied a transmission problem, set in unbounded domain
composed of a half line and a thin layer, under the ellipticity assumption. The right-hand
term of the equation is a Hölder continuous function.
