Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces

By Haim Brezis, Petru Mironescu. 2001

224 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1d5291f1061887e1a15c5a32a158bb52568bc075

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In Applied Mathematics

Citations in the corpus

Sharp embedding results for spaces of smooth functions with power weights (2011, methodology): “ve that q 0 ≤ q 1. Hence (1.2) is valid. 5. Embeddingsfor Triebel-Lizorkinspaces – Proofof Theorem 1.2 5.1. Suﬃcient conditions. In the proof of the suﬃciency part of Theorem 1.2 we employ ideas from [7] and [38]. One has the following Gagliardo-Nirenberg type inequality for spaces with weights. 18 ”
Continuous dependence for NLS in fractional order spaces (2010, background): “) On the other hand, few works study the continuity of such maps, among which [2, 3, 4, 5, 6], but none of these works applies to such cases as g(u) = |u|u, which is a typical nonlinearity for (NLS).”
On the Regularity of Minima of Non-autonomous Functionals (2019, methodology): “In fact, the inequality we are going to use here requires the use of certain Gagliardo-Nirenberg inequalities in Triebel-Lizorkin spaces, as explained in [7, 8].”
Hitchhiker's guide to the fractional Sobolev spaces (2011, methodology): “obtained by interpolation techniques and by passing through Besov spaces; see, for instance, [6, 7, 95, 96, 63]. For a more comprehensive treatment of fractional Sobolev-type inequalities we refer to [61, 62, 12, 1, 91] and the references therein. We remark that the proof here is self-contained. Mor”
Gradient regularity in mixed local and nonlocal problems (2022, methodology): “On the other hand, if sγ = p , we use [13, Corollary 3.2, (c)], that is , that holds whenever θ ∈ (0 , 1) , where c ≡ c ( n, σ, λ, θ ) .”
H1/2 maps with values into the circle: Minimal Connections, Lifting, and the Ginzburg–Landau equation (2004, background): “[21]) ‖va,ε‖H1/2 ≤ C‖va,ε‖ L p′ ‖va,ε‖ W1,p .”
Gagliardo–Nirenberg inequalities and non-inequalities: The full story (2017, unknown): “…s < ∞ , p = 1 and 1 < p ≤ ∞ when s and s are not integers (with a proof involving wavelets) ii) A result of Oru [11] (unpublished; for a proof, see [3, Section III]) yields in full generality the case 0 ≤ s < s < ∞ , 1 < p 1 < ∞ and 1 < p 2 < ∞ and also implies the validity of (1.10) in some…”