Characterization of polynomials and higher-order Sobolev spaces in terms of functionals involving difference quotients

Rita Ferreira*, Carolin Kreisbeck, Ana Margarida Ribeiro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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 Wk,p(Ω), k∈N and p∈(1,+∞), for arbitrary open sets Ω⊂ℝn. In particular, we provide natural generalizations of the results regarding Sobolev spaces summarized in Brézis' overview article [Brézis (2002)] to the higher-order case, and extend the work [Borghol (2007)] to a more general setting.

Original languageEnglish (US)
Pages (from-to)199-214
Number of pages16
JournalNonlinear Analysis, Theory, Methods and Applications
Volume112
DOIs
StatePublished - Jan 1 2015

Keywords

  • Higher-order Sobolev spaces
  • Singular functionals

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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