Translator Disclaimer
January/February 2010 Transmission problem for an abstract fourth-order differential equation of elliptic type in UMD spaces
Angelo Favini, Rabah Labbas, Keddour Lemrabet, Stéphane Maingot, Hassan Diaramouna Sidibé
Adv. Differential Equations 15(1/2): 43-72 (January/February 2010).

Abstract

In this work, we present a new result ofexistence, uniqueness and maximal regularity for the restriction solutions of the bilaplacian transmission problem set in the juxtaposition of two rectangular bodies. The study is performed in the space $L^{p}( (-1, 0) \cup(0, \delta) ;X),$ $1 < p < \infty,$ where $\delta $ is a small parameter which is destined to tend to zero and $X$ is a UMD Banach space. The geometry of the bodies allows us to find an explicit representation of the solutions in virtue of the operational Dunford calculus. We then use essentially the famous Dore-Venni theorem among others for the analysis of the solutions.

Citation

Download Citation

Angelo Favini. Rabah Labbas. Keddour Lemrabet. Stéphane Maingot. Hassan Diaramouna Sidibé. "Transmission problem for an abstract fourth-order differential equation of elliptic type in UMD spaces." Adv. Differential Equations 15 (1/2) 43 - 72, January/February 2010.

Information

Published: January/February 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1194.35128
MathSciNet: MR2588389

Subjects:
Primary: 35C15, 35J30, 35J40, 45N05

Rights: Copyright © 2010 Khayyam Publishing, Inc.

JOURNAL ARTICLE
30 PAGES


SHARE
Vol.15 • No. 1/2 • January/February 2010
Back to Top