The sharp quantitative Sobolev inequality for functions of bounded variation

By N. Fusco, Francesco Maggi, Aldo Pratelli. 2007

62 citations recorded by the source corpus.

Abstract The classical Sobolev embedding theorem of the space of functions of bounded variation BV ( R n ) into L n ′ ( R n ) is proved in a sharp quantitative form.

Subfields: Applied Mathematics, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/205fb1c601711fe2abffc759e354380579a25cb8

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In Applied Mathematics

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (2022, background): “In fact, stability has attracted a lot of attention in recent years and we refer to [44, 26, 39, 27, 23, 30, 21, 24, 38, 25, 61, 42, 43, 40, 10] and the references within for a list of works in this direction.”
Some methods for studying stability in isoperimetric type problems (2008, background): “There are many relevant variational problems [PS, Ka] intimately related to the same symmetrization inequalities studied here from a quantitative point of view, and these ideas have already been shown to be flexible enough to be employed in the study of quantitative forms of other variational proble”
Asymmetric affine Lp Sobolev inequalities (2009, background): “In recent years, many variations and generalizations have been obtained, see, e.g., [2, 3, 6, 8, 11 , 32, 33, 37] and the references therein.”
Sharp gradient stability for the Sobolev inequality (2020, methodology): “These technique were further developed by Figalli, Maggi, and Pratelli in [23] to provide a sharp stability result —both in terms of the notion of distance and of the decay exponent— in the special case p = 1 (for this case, see also the earlier results [8, 26, 27]).”
The sharp Sobolev inequality in quantitative form (2009, methodology): “We want now to prove that, when f is positive, then the inflma deflning ‚(f) and ‚(fjS) are attained; this proof closely reminds the proof of Lemma B.1 in [ FMP2 ], and we will obtain it in two steps.”
The sharp quantitative isoperimetric inequality (2008, methodology): “This application is contained in the forthcoming paper [14] by the same authors.”
A Selection Principle for the Sharp Quantitative Isoperimetric Inequality (2010, background): “Since the publication of [19] the study of quantitative forms of various geometric and functional inequalities has received a new impulse (see for instance [18], [20], [13], [14], [8] and the review paper [26]).”
Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller–Segel equation (2011, background): “Moreover, other recent proofs for stability based on optimal transportation [17] or symmetrization techniques [19, 20, 13, 18] did not produce (at least up to now) any results in this situation.”