Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation

85 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Quantitative logarithmic Sobolev inequalities and stability estimates (2014, result): “But ∫ R |(log f)′ − b|2dν is the relative Fisher information of ν with respect to the non-centered Gaussian dγb = e b.x−b2/2dγ which satisfies a logarithmic Sobolev inequality with constant 12 .”
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]).”
Anisotropic fractional Sobolev norms (2013, background): “e set kfk W1,p,K = Z Rn k∇f(x)kp K∗ dx 1/p , where K∗ = {v ∈ Rn : v · x ≤ 1 for all x ∈ K} is the polar body of K. Anisotropic Sobolev seminorms have attracted increased interest in recent years (cf. [1,5,9,13]). A natural question is to study the limiting behavior of anisotropic s-seminorms as s → ”
Anisotropic fractional perimeters (2013, unknown): “Anisotropic perime-ters correspond to anisotropic Sobolev seminorms which have been studied in numerous papers (cf. [ 2, 9, 13, 18] and the references therein).”
A Sharp Stability Result for the Relative Isoperimetric Inequality Inside Convex Cones (2012, background): “In general, sets for which τ(E) > 1 enjoy a nontrivial Sobolev-Poincaré type inequality (see [16, Lemma 3.1]).”