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 |