This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Ferreira, RitaKreisbeck, CarolinRibeiro, Ana Margarida2016-03-242019-06-2820142198-5855https://doi.org/10.34657/2112https://oa.tib.eu/renate/handle/123456789/2965The aim of this paper, which deals with a class of singular functionals involving difference quotients, is twofold: deriving suitable integral conditions under which a measurable function is polynomial and stating necessary and sufficient criteria for an integrable function to belong to a kth-order Sobolev space. One of the main theorems is a new characterization of Wk,p (Omega), k N and p (1,+∞), for arbitrary open sets Omega Rn. In particular, we provide natural generalizations of the results regarding Sobolev spaces summarized in Brézis overview article [Russ. Math. Surv. 57 (2002), pp. 693-708] to the higher-order case, and extend the work by Borghol [Asymptotic Anal. 51 (2007), pp. 303-318] to a more general setting.application/pdfeng510Higher-order Sobolev spacesnonlocal functionalsReport