Functions of Bounded Variation¶and Rearrangements

By Andrea Cianchi, N. Fusco. 2002

105 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8e56da757d4b7b3c3f3455618d87b4cb2ac972da

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In Applied Mathematics

Citations in the corpus

Faber–Krahn Inequalities for the Robin-Laplacian: A Free Discontinuity Approach (2015, background): “Up to our knowledge, the only result in the literature concerning rearrangements in presence of trace terms (treated as jumps) is due to Cianchi and Fusco [8], and requires a linear growth in the gradient term of the functional, which is not the case for (1.”
Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities (2009, unknown): “It is shown by the Coarea Formula (see [5, 9]) that the absolutely continuous part of the distributional derivative of μ has a (non positive) density μ′(t) satisfying −μ′(t)= ∫ { f =t} dH n−1 |∇ f | ≥ ∫ { f =t} dH n−1 |∇ f | , for a.”
The quantitative isoperimetric inequality and related topics (2015, background): “The equality cases in the Pólya–Szegö inequality have been fully characterized first by Brothers and Ziemer in [28], see also [61, 41].”
The sharp Sobolev inequality in quantitative form (2009, background): “a.e. t > 0, and equality holds in the second inequality since also (3.12) turns into an equality in this case (see e.g. [ CF1 , Lemma 3.2]).”
An asymmetric affine Pólya–Szegö principle (2012, unknown): “, [9,16,19–22,28,31]).”
The Faber–Krahn inequality for the short-time Fourier transform (2021, background): “…speaking it does not belong to W 1 , 1 ( R 2 ), which would require to ﬁx a lot of details when referring to the general results from [6, 13, 15]), here we present an elementary and self-contained proof of this lemma, specializing to our case a general argument from [13] based on the coarea…”