Zusammenfassung
The 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 W-k,W-p (Omega), k is an ...
Zusammenfassung
The 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 W-k,W-p (Omega), k is an element of N and p is an element of (1,+ infinity), for arbitrary open sets Omega subset of R-n. In particular, we provide natural generalizations of the results regarding Sobolev spaces summarized in Brezis' overview article [Brezis (2002)] to the higher-order case, and extend the work [Borghol (2007)] to a more general setting. (C) 2014 Elsevier Ltd. All rights reserved.
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