Weighted fractional Poincaré inequalities via isoperimetric inequalities
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2024-11
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Language
en
Pages
32
Series
Calculus of Variations and Partial Differential Equations, Volume 63, issue 8, pp. 1-32
Abstract
Our main result is a weighted fractional Poincaré–Sobolev inequality improving the celebrated estimate by Bourgain–Brezis–Mironescu. This also yields an improvement of the classical Meyers–Ziemer theorem in several ways. The proof is based on a fractional isoperimetric inequality and is new even in the non-weighted setting. We also extend the celebrated Poincaré–Sobolev estimate with Ap weights of Fabes–Kenig–Serapioni by means of a fractional type result in the spirit of Bourgain–Brezis–Mironescu. Examples are given to show that the corresponding Lp-versions of weighted Poincaré inequalities do not hold for p>1.Description
Publisher Copyright: © The Author(s) 2024.
Keywords
42B25, 46E35
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Citation
Myyryläinen, K, Pérez, C & Weigt, J 2024, ' Weighted fractional Poincaré inequalities via isoperimetric inequalities ', Calculus of Variations and Partial Differential Equations, vol. 63, no. 8, 205, pp. 1-32 . https://doi.org/10.1007/s00526-024-02813-6