A biharmonic transmission problem in <i>L^p</i>-spaces

In this work we study, by a semigroup approach, a transmission problem based on biharmonic equations with boundary and transmission conditions, in two juxtaposed habitats. We give a result of existence and uniqueness of the classical solution in \begin{document}$ L^p $\end{document} -spaces, for \begin{document}$ p \in (1,+\infty) $\end{document} , using analytic semigroups and operators sum theory in Banach spaces. To this end, we invert explicitly the determinant operator of the transmission system in \begin{document}$ L^p $\end{document} -spaces using the \begin{document}$ \mathcal{E}_{\infty} $\end{document} -calculus and the Dore-Venni sums theory.