The core-radius approach to supercritical fractional perimeters, curvatures and geometric flows

Luca, Lucia De; Kubin, Andrea; Ponsiglione, Marcello

doi:10.1016/j.na.2021.112585

Cited by 5 publications

(1 citation statement)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The analysis of the asymptotic behavior in the sense of Γ-convergence [8] of the fractional perimeter functionals introduced in [7] was undertaken in [2], and then extended in multiple directions by several contributions, e.g. [4,10,14,17]. Finally, we point Date: February 14, 2023. out that a general variational framework for the analysis of (static and dynamic) multiscale problems that feature nonlocal interactions has been very recently considered in the monograph [1], again for kernels that, in our notation, are required to form a definitively bounded sequence in L 1 .…”

Section: Introductionmentioning

confidence: 99%

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

Dai

Grafakos²,

Pan³

et al. 2023

Math. Ann.

View full text Add to dashboard Cite

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.

show abstract