Characterizations of second order Sobolev spaces. (July 2015)

• Record Type: Journal Article
• Authors: Cui, Xiaoyue; Lam, Nguyen; Lu, Guozhen
• Is Part Of: Nonlinear analysis. Volume 121(2015)
• Page Start: 241
• Page End: 261
• Publication Date: 2015-07
• Subjects: Characterizations -- Second order Sobolev spaces -- Second order differences -- Taylor remainder of first order -- Hardy–Littlewood maximal functions -- Mean-value formulas; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.01.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Second order Sobolev spaces are important in applications to partial differential equations and geometric analysis, in particular to equations such as the bi-Laplacian. The main purpose of this paper is to establish some new characterizations of the second order Sobolev spaces W 2, p ( R N ) in Euclidean spaces. We will present here several types of characterizations: by second order differences, by the Taylor remainder of first order and by the differences of the first order gradient. Such characterizations are inspired by the works of Bourgain et al. (2001) and Nguyen (2006, 2008) on characterizations of first order Sobolev spaces in the Euclidean space.