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

Abstract

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 L p -spaces, for p ∈ (1, +∞), using analytic semigroups and operators sum theory in Banach spaces. To this end, we invert explicitly the determinant operator of the transmission system in L p -spaces using the E∞-calculus and the Dore-Venni sums theory.