A biharmonic transmission problem in Lp-spaces

TL;DR

This paper investigates a biharmonic transmission problem in Lp-spaces, establishing existence and uniqueness of classical solutions using semigroup theory, operator calculus, and explicit inversion of the transmission operator.

Contribution

It introduces a novel semigroup approach to solve biharmonic transmission problems in Lp-spaces, employing advanced operator calculus techniques.

Findings

Proved existence and uniqueness of solutions in Lp-spaces.

Explicitly inverted the transmission operator using E∞-calculus.

Applied semigroup and operator sum theory to boundary value problems.

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 $\in$ (1, +$\infty$), 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 $\infty$-calculus and the Dore-Venni sums theory.