Lifting in Sobolev spaces

By Jean Bourgain, Haim Brezis, Petru Mironescu. 2000

203 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ed71dd003e17829f91207289a21db4e7f5d680ad

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations (2014, background): “In the theory of lifting of fractional Sobolev maps into the unit circle [17], Theorem 1.”
Embeddings for A-weakly differentiable functions on domains (2017, background): “rks [6, 8] that, for Poisson’s equation in Rn, n ≥ 2, ∆u = f, the surprising strong L1–estimate kDukL1∗ 6 ckfkL1 holds provided that f ∈ C∞ c is divergence–free. This and substantial contributions in [9, 10, 11, 5, 7, 6, 8, 52, 53, 54, 55] lead to the remarkable characterization by Van Schaftingen [”
Lifting of BV functions with values in S1 (2003, methodology): “A complete description for the existence of the lifting in general Sobolev sp Ws,p(Ω;S1), 0< s < ∞ and 1< p < ∞, was given later by Bourgain, Brezis and Mironescu [4].”
A new approach to Sobolev spaces and connections to $\mathbf\Gamma$-convergence (2004, unknown): “Given ω : [0,∞) → [0,∞) continuous, we define ωµ(v) := ∫ SN−1 ω ( |v · σ| ) dµ(σ) ∀v ∈ RN .”
Limiting embedding theorems forWs,p whens ↑ 1 and applications (2002, background): “of a result announced in [ 2 ] (Remark E. 1). Namely, on f~ = (- 1, + 1), consider the function”
The Fundamental Theorem of Surface Theory for Surfaces with Little Regularity (2003, background): “Such an open set is connected if and only if, for all x, y ∈ , there exists a path joining x to y. The set is simply-connected if, for all γ0, γ1 ∈ C 0 ([0, 1]; ) such that γ0(0) = γ1(0) and γ0(1) = γ1(1), there exists a homotopy joining γ0 to γ1, i.e., an application ϕ ∈ C 0 ([0, 1 ]×[ 0, 1]; ) s”
Functions with prescribed singularities (2003, background): “[15], see also [8], [11] for more general results).”