On an open question about functions of bounded variation

By J. D'avila. 2002

285 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/13f9507cfb72a1955752c7b55b48aca54e5ba4ca

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Citations in the corpus

Nonlocal quantitative isoperimetric inequalities (2015, background): “In particular, according [10, Theorem 1] (see also [7, 14, 3]), we have that the fractional perimeter Pα, if suitably renormalized, approaches the classical perimeter P as α↗ 1.”
Anisotropic fractional Sobolev norms (2013, result): “For p = 1, it follows from [2, Theorem 3’] that a corresponding result holds for f 6∈ BV (R) (see also Dávila [6]).”
Characterization of Sobolev and BV Spaces (2011, methodology): “[34] J.D. Dávila, On an open question about functions of bounded variation.”
A new approach to Sobolev spaces and connections to $\mathbf\Gamma$-convergence (2004, unknown): “Given ω : [0,∞) → [0,∞) continuous, we define ωµ(v) := ∫ SN−1 ω ( |v · σ| ) dµ(σ) ∀v ∈ RN .”
Fractional p-Laplacian evolution equations (2016, unknown): “4) In [10] and [18] it is proved that, for u ∈W (Ω) if p > 1, and for u ∈ BV (Ω) if p = 1, lim n→∞ Ψ sn (u) = Ψ (u), (7.”
Anisotropic fractional perimeters (2013, unknown): “(18) Extending a result by Bourgain, Brezis & Mironescu [5] from W (1,1)(R) to BV (R), Dávila [10] proved that for f ∈ BV (R), lim s→1 (1− s)‖f‖W s,1 = 2αn ‖f‖BV , (19) where αn is the constant from (1), the vector valued Radon measure Df is the weak gradient of f , and ‖f‖BV is the total variation ”
Localization of nonlocal gradients in various topologies (2015, methodology): “In particular, in this paper we show the nonlocal gradient analogy to localization in and characterization of Sobolev spaces [5], of BV spaces [12], and in the sense of Γ-convergence [22].”
The quantitative isoperimetric inequality and related topics (2015, background): “It was completed by Dávila [52], see also [115] for a simpler proof.”