A biharmonic transmission problem in Lp-spaces

Alexandre Thorel (1)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

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.

Mots clés: Analytic semigroups; biharmonic equations; functional calculus; Interpolation spaces

Domaines: Mathématiques [math]; Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Alexandre Thorel. A biharmonic transmission problem in Lp-spaces. 2020. ⟨hal-02927622v1⟩