A biharmonic transmission problem in Lp-spaces

Alexandre Thorel

doi:10.3934/cpaa.2021102

Article Contents

2021, Volume 20, Issue 9: 3193-3213. Doi: 10.3934/cpaa.2021102

This issue Previous Article Riesz-type representation formulas for subharmonic functions in sub-Riemannian settings Next Article Fractional Yamabe solitons and fractional Nirenberg problem

A biharmonic transmission problem in L^p-spaces

Alexandre Thorel^,

Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France

^* Corresponding author
^* Corresponding author

Received: February 28, 2021

Revised: April 30, 2021

Early access: June 2021

Published: September 2021

This research is supported by CIFRE contract 2014/1307 with Qualiom Eco company and partially by the LMAH and the european funding ERDF through grant project Xterm

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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 $ \mathcal{E}_{\infty} $-calculus and the Dore-Venni sums theory.

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Mathematics Subject Classification: 35B65, 35J48, 35R20, 47A60, 47D06.

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