A biharmonic transmission problem in Lp-spaces

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M2">\begin{document}$ L^p $\end{document}</tex-math></inline-formula>-spaces, for <inline-formula><tex-math id="M3">\begin{document}$ p \in (1,+\infty) $\end{document}</tex-math></inline-formula>, using analytic semigroups and operators sum theory in Banach spaces. To this end, we invert explicitly the determinant operator of the transmission system in <inline-formula><tex-math id="M4">\begin{document}$ L^p $\end{document}</tex-math></inline-formula>-spaces using the <inline-formula><tex-math id="M5">\begin{document}$ \mathcal{E}_{\infty} $\end{document}</tex-math></inline-formula>-calculus and the Dore-Venni sums theory.</p>