Nonlinear flows allow to cover the interval of exponents ranging from Poincaré to Sobolev inequality, while an intriguing limitation (an upper bound on the exponent) appears in the carré du champ method based on the heat flow. We investigate this limitation, describe a counter-example for ...
Interpolation InequalitiesThe purpose of this Chapter is to give some results which extend known inequalities in a systematic way by interpolating the extremes. As a simple example we cite the AG inequality 1.doi:10.1007/978-94-017-1043-5_29DS Mitrinovi'cJE Pevcari'c...
In the simplest case, linear interpolation, the value of f(x) at a point x satisfying the inequality x0 < x1, is taken to be equal to the value of the linear function coinciding with f(x) at the points x = x0 and x = x1. The interpolation problem is undefined from a strict ma...
work of Nirenberg His significant contributions included the Gagliardo-Nirenberg interpolation inequality (with Emilio Gagliardo). In addition, he mentored numerous graduate students (46 mathematicians studied under him).
5)polynomial interpolation inequality多项式内插不等式 6)bilinear polynomial interpolation双线性多项式内插 1.This paper established interpolation model for calculating the ground settlement value of the unknown points using polyhedral function method,the weighted average method,the linear interpolation method,and...
Here we prove that symmetry can be broken even within the set of parameters where radial extremals correspond to local minima for the variational problem associated with the inequality. For interpolation inequalities, such a symmetry breaking phenomenon is entirely new....
logarithmic Sobolev inequalityheat equationhypercontractivityspectral decompositionThis paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range ...
In this work we are concerned with the minimization problem associated to the best constant Cn,α in the following interpolation inequality ∫∫|u(x)|α|u(y)|α|x-y|n-2dxdy≤Cn,α|∇ψ|L2nα-(n+2)|ψ|L2(n+2)-(n-2)α, u∈H1(Rn) for 2≤α-Δu+ωu-(|x|-(n-2)*|...
We then consider the associated entropic Ricci curvature lower bound via the geodesic convexity of p -divergence, and obtain an HWI-type interpolation inequality. This enables us to prove that the positive Ricci curvature implies the quantum Beckner's inequality, from which a transport cost and ...
A simple particular case corresponding to \\\(n = 1\\\) and \\\(\\\omega \\\left( r ight) = r\\\) is the Landau type inequality \\\(\\\left| {u'\\\left( x ight)} ight|^2 \\\leqslant \\\frac{8}{3}\\\mathcal{M}^\\\diamondsuit u\\\left( x ight)\\\mathcal{...