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Estimations polynomiales pour les problèmes de transmission sur des domaines à bords plats

Hassan Mohsen, Simon Labrunie and Victor Nistor

Vol. 4 (2022), No. 4, 755–777
Abstract

Nous traitons des opérateurs elliptiques du second ordre P dont les coefficients sont vus comme des variables aléatoires. Notre but est d’obtenir des estimations de leurs solutions qui soient polynomiales dans les coefficients. Ces estimations sont utiles pour la quantification de l’incertitude. Nous traitons ici le cas dans lequel le bord et l’interface sont parallèles aux hyperplans {xm = 0} m.

We study second-order elliptic operators P whose coefficients are regarded as random variables. Our goal is to obtain estimations of their solutions that are polynomial in the coefficients of the operator. These estimations are useful for uncertainty quantification. Here, we will treat the case where the boundary and interface are parallel to the hyperplanes {xm = 0} m.

Keywords
parametric elliptic equations, Sobolev spaces, Laplace operator, transmission problem, mixed boundary value problem, uncertainty quantification
Mathematical Subject Classification
Primary: 35R60
Secondary: 35J25, 60H35
Milestones
Received: 15 March 2022
Accepted: 14 July 2022
Published: 15 January 2023
Authors
Hassan Mohsen
IECL
Université de Lorraine
Villers-lès-Nancy
France
Simon Labrunie
IECL
Université de Lorraine
Villers-lès-Nancy
France
Victor Nistor
Département de mathématiques
Université de Lorraine
Metz
France