The fractional variation and the precise representative of BVα,p functions

Giovanni E. Comi, Daniel Spector, Giorgio Stefani*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We continue the study of the fractional variation following the distributional approach developed in the previous works Bruè et al. (2021), Comi and Stefani (2019), Comi and Stefani (2019). We provide a general analysis of the distributional space BVα,p(Rn) of Lp functions, with p∈ [1 , + ∞] , possessing finite fractional variation of order α∈ (0 , 1). Our two main results deal with the absolute continuity property of the fractional variation with respect to the Hausdorff measure and the existence of the precise representative of a BVα,p function.

Original languageEnglish
Pages (from-to)520-558
Number of pages39
JournalFractional Calculus and Applied Analysis
Volume25
Issue number2
DOIs
Publication statusPublished - 2022 Apr

Keywords

  • Fractional capacity
  • Fractional divergence
  • Fractional gradient
  • Fractional variation
  • Hausdorff measure
  • Precise representative

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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