Compactness for Sobolev-type trace operators. (June 2019)

• Record Type: Journal Article
• Authors: Cavaliere, Paola; Mihula, Zdeněk
• Is Part Of: Nonlinear analysis. Volume 183(2019)
• Page Start: 42
• Page End: 69
• Publication Date: 2019-06
• Subjects: 46E35 -- 46E30; Sobolev spaces -- Trace embeddings -- Optimal target -- Rearrangement-invariant spaces -- Lorentz spaces -- Orlicz spaces -- Supremum operators; 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.2019.01.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Compactness of arbitrary-order Sobolev type embeddings for traces of n -dimensional functions on lower dimensional subspaces is investigated. Sobolev spaces built upon any rearrangement-invariant norm are allowed. In particular, we characterize compactness of trace embeddings for classical Sobolev, Lorentz–Sobolev and Orlicz–Sobolev type spaces.