Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities

Following the seminal paper by Bourgain, Brezis and Mironescu, we focus on the asymptotic behavior of some nonlocal functionals that, for each u ∈ L 2 (R N ), are defined as the double integrals of weighted, squared difference quotients of u. Given a family of weights {ρε}, ε ∈ (0, 1), we devise sufficient and necessary conditions on {ρε} for the associated nonlocal functionals to converge as ε → 0 to a variant of the Dirichlet integral. Finally, some comparison between our result and the existing literature is provided.

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Generalized Brezis–Seeger–Van Schaftingen–Yung formulae and their applications in ball Banach Sobolev spaces

Zhu,

Yang,

Yuan

2023

Calc. Var.

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Brezis–Van Schaftingen–Yung formulae in ball Banach function spaces with applications to fractional Sobolev and Gagliardo–Nirenberg inequalities

Cited by 17 publications

References 92 publications

Functional Inequalities in Stratified Lie Groups with Sobolev, Besov, Lorentz and Morrey Spaces

Functional Inequalities in Stratified Lie Groups with Sobolev, Besov, Lorentz and Morrey Spaces

The Bourgain–Brezis–Mironescu formula on ball Banach function spaces

Generalized Brezis–Seeger–Van Schaftingen–Yung formulae and their applications in ball Banach Sobolev spaces

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