A sharp Sobolev trace inequality for the fractional-order derivatives

By Jie Xiao. 2006

53 citations recorded by the source corpus.

We establish a sharp Sobolev trace inequality for the fractional-order derivatives. As a close connection with this best estimate, we show a fractional-order logarithmic Sobolev trace inequality with the asymptotically optimal constant, but also sharpen the Poincare embedding for the conformal invariant energy and BMO spaces.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e60beef35134e6e12b4130cbe42f32455091ce59

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

A concave—convex elliptic problem involving the fractional Laplacian (2010, unknown): “rom the proof of the local characterization of (−∆)α/2 in [17]. The calculations performed in [17] can be extended to cover the range α/2 <β<2 and in particular includes the case β= 1 proved in [42]. Proof. Since z= Eβ(v), by deﬁnition zsolves div(y1−β∇z) = 0, which is equivalent to ∆xz+ 1−β y”
Well‐posedness for fractional Navier–Stokes equations in the largest critical spaces Ḃ∞,∞−(2β−1)(Rn) (2012, background): “Rn/ studied in Essen et al. [27], Xiao [28], and Dafni and Xiao [29].”
ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR ELLIPTIC PROBLEMS WITH THE FRACTIONAL LAPLACIAN (2013, unknown): “[36]).”
Fractional Gagliardo–Nirenberg and Hardy inequalities under Lorentz norms (2012, background): “Xiao in [24] proved that, for u ∈ Ḣs(Rn−1) with ∥u∥L2(Rn−1) = 1,”
Existence theorems of the fractional Yamabe problem (2016, methodology): “Besides an application of the Sobolev inequality and the Sob olev trace inequality (see [17, 45]) yields (∫”