Sentence examples for sharp constant from inspiring English sources

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces.

Explicit expressions of the sharp constant, as well as minimizers, are established in the radial case.

We then prove that Hardy inequalities with a sharp constant hold on weakly mean convex C2 domains.

From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale.

A quantitative version of the standard Sobolev inequality, with sharp constant, for functions u in W1,1(Rn) (or BV(Rn)) is established in terms of a distance of u from the manifold of all multiples of characteristic functions of balls.

We prove the following inequality with a sharp constant,‖P+f‖p(T ⩽csc  ‖f‖p(T),  f∈Lp(T),where 1

Sharp constants and some extended versions are put forward.

However, when no symmetry is imposed, the sharp constants are not achieved by radial functions, in some range of the parameters.

We compute the limits of higher-order Besov norms and derive the sharp constants for certain forms of the Sobolev embedding theorem.

As a consequence we give sharp constants to measure the attractive part of the potential and its rate of decay, which turns out to be different whether dimension 3 or higher are considered.

We also prove an analogous inequality in the nonperiodic case where P+f=F−1 (χR+Ff) is the half-line Fourier multiplier on R. Similar weighted inequalities with sharp constants for Lp R, |x|α), −1<α