Another look at Sobolev spaces

By Jean Bourgain, Haim Brezis, Petru Mironescu. 2001

684 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/90fd46546a9bba8ba402086748c57da036c42408

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Citations in the corpus

On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity (2007, background): “[11] relating the H(1)-norm of a function to a double integral over divided differences of the function is employed.”
On the definition and the properties of the principal eigenvalue of some nonlocal operators (2015, unknown): “∫ RN ρσ(z)dz = 1, ∀σ > 0, limσ→0 ∫ |z|≥δ ρσ(z)dz = 0, ∀ δ > 0, which, from the characterisation of Sobolev spaces in [13, 14, 55], enforces that lim σ→0 ∫∫”
Gagliardo-Nirenberg, composition and products in fractional Sobolev spaces (2001, unknown): “In view of the results in [8], one may expect an inequality of the form ‖f‖W s/2,2p ≤ C(p)(1− s) ‖f‖ 1/2 W s,p‖f‖ 1/2 L as s ր 1, if we take the Gagliardo norms (4).”
Characterization of Sobolev and BV Spaces (2011, methodology): “In one dimension, Bourgain, Brezis, and Mironescu were able to obtain C1 = C2 = 1, so that the BV semi-norm is actually the limit as in the W 1,p case.”
Hitchhiker's guide to the fractional Sobolev spaces (2011, background): “i=1 ∫ Sn−1 |ξi| (2)dσ(ξ) = ωn−1 2n and C2 = ωn−1 (see [11] and [66]).”
Stability of variational eigenvalues for the fractional p−Laplacian (2015, methodology): “By using Theorem 3.1, we can prove a dual version of the Bourgain-Brezis-Mironescu result.”
A nonlocal p-Laplacian evolution equation with Neumann boundary conditions (2008, unknown): “Following [12], to prove 2 it is enough to show that for any δ > 0 there exists nδ ∈ N such that δ−N δ ∫”
Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori (2015, methodology): “It originated from [14] in which Bourgain, Brézis and Mironescu proved that for any 1 ≤ p <∞ and any f ∈ C∞ 0 (R)”
Global existence of weak solutions for compressible Navier--Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor (2015, methodology): “nt method than the one introduced here. Those estimates correspond to critical spaces, also developed and used for instance in works by J. Bourgain, H. Br´ezis and P. Mironescu and by A.C. Ponce, see [12] and [60]. Because of the weak regularity of the velocity ﬁeld, the corresponding norm of the cr”
A new characterization of Sobolev spaces (2006, unknown): “Hence |[t1,j − 4λ1,j , t1,j + 4λ1,j ] ∩ Bj | = 0 or |[t1,j − 4λ1,j , t1,j + 4λ1,j ] \ Bj | = 0 (see [3]).”