Ferreira, Rita and Kreisbeck, Carolin and Ribeiro, Ana Margarida (2015) Characterization of polynomials and higher-order Sobolev spaces in terms of functionals involving difference quotients. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 112. pp. 199-214. ISSN 0362-546X, 1873-5215
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | RECOGNIZE CONSTANT FUNCTIONS; Higher-order Sobolev spaces; Singular functionals |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Aug 2019 07:52 |
| Last Modified: | 05 Aug 2019 07:52 |
| URI: | https://pred.uni-regensburg.de/id/eprint/6394 |
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