Sobolev spaces and Poincaré inequalities on the Vicsek fractal

Fabrice Baudoin*, Li Chen

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

7 Citations (Scopus)

Abstract

In this paper we prove that several natural approaches to Sobolev spaces coincide on the Vicsek fractal. More precisely, we show that the metric approach of Korevaar–Schoen, the approach by limit of discrete p-energies and the approach by limit of Sobolev spaces on cable systems all yield the same functional space with equivalent norms for p > 1. As a consequence we prove that the Sobolev spaces form a real interpolation scale. We also obtain Lp-Poincaré inequalities for all values of p ≥ 1.

Original languageEnglish
JournalAnnales Fennici Mathematici
Volume48
Issue1
Pages (from-to)3-26
Number of pages24
ISSN2737-0690
DOIs
Publication statusPublished - 2022
Externally publishedYes

Keywords

  • P-energies
  • Poincaré inequalities
  • Real interpolation
  • Sobolev spaces
  • Vicsek set

Fingerprint

Dive into the research topics of 'Sobolev spaces and Poincaré inequalities on the Vicsek fractal'. Together they form a unique fingerprint.

Cite this