Abstrakti
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.
| Alkuperäiskieli | Englanti |
|---|---|
| Artikkeli | 205 |
| Sivut | 1-32 |
| Sivumäärä | 32 |
| Julkaisu | Calculus of Variations and Partial Differential Equations |
| Vuosikerta | 63 |
| Numero | 8 |
| DOI - pysyväislinkit | |
| Tila | Julkaistu - marrask. 2024 |
| OKM-julkaisutyyppi | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä |
Rahoitus
The research was supported by the Academy of Finland. K. Myyryläinen and J. Weigt have also been supported by the Magnus Ehrnrooth Foundation. C. Pérez is supported by grant PID2020-113156GB-I00, Spanish Government; by the Basque Government through grant IT1615-22 and the BERC 2014-2017 program and by the BCAM Severo Ochoa accreditation CEX2021-001142-S, Spanish Government. J. Weigt is also supported by the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 948021). We are very grateful to the Department of Mathematics at Aalto University for its support where the initiation of this research took place. In particular, we are very grateful to Juha Kinnunen for his support and for the discussions we had.