Related papers: The Coarea Inequality
The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.
We obtain exact conditions guaranteeing that any global weak solution of the differential inequality $$ \sum_{|\alpha| = m} \partial^\alpha a_\alpha (x, u) \ge g (|u|) \quad \mbox{in } {\mathbb R}^n $$ is trivial, where $m, n \ge 1$ are…
We prove logarithmic Sobolev inequalities on higher-dimensional bounded smooth domains based on novel Gagliardo-Nirenberg type interpolation inequalities. Moreover, we use them to address the long-time dynamics of some nonlinear nonlocal…
Our main purpose is to establish Gagliardo-Nirenberg type inequalities using fractional homogeneous Sobolev spaces, and homogeneous Besov spaces. In particular, we extend some of the results obtained by the authors in [1, 2, 3, 7, 16, 21].
It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…
Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and…
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
Cheeger inequality is a classical result emerging from the isoperimetric problem in the field of geometry. In the graph theory, a discrete version of Cheeger inequality was also studied deeply and the notion was further extended for higher…
The discrete isoperimetric inequality states that among all n -gons with a fixed area, the regular n -gon has the least perimeter. We prove analogues of the discrete isoperimetric inequality (involving circumradius or inradius) for cyclic…
We study the Riemannian quantiative isoperimetric inequality. We show that direct analogue of the Euclidean quantitative isoperimetric inequality is--in general--false on a closed Riemannian manifold. In spite of this, we show that the…
This note provides the generalization of a remarkable inequality by A. C. Ponce whose consequences are essential in several fields, as Characterization of Sobolev Spaces or Nonlocal Modelization.
In this article, we have derived the following Leray-Trudinger type inequality on a bounded domain $\Omega$ in $\mathbb{R}^n $ containing the origin. \begin{align*} \displaystyle{\sup_{u\in W^{1,n}_{0}(\Omega), I_{n}[u,\Omega,R]\leq…
Ratios of quantiles are often computed for income distributions as rough measures of inequality, and inference for such ratios have recently become available. The special case when the quantiles are symmetrically chosen; that is, when the…
There is a need in general relativity for a consistent and useful mathematical theory defining the multiplication of tensor distributions in a geometric (diffeomorphism invariant) way. Significant progress has been made through the concept…
We present a short proof of a conjecture proposed by I. Ra\c{s}a (2017), which is an inequality involving basic Bernstein polynomials and convex functions. This proof was given in the letter to I. Ra\c{s}a (2017). The methods of our proof…
Keller packings and tilings of boxes are investigated. Certain general inequality measuring a complexity of such systems is proved. A straightforward application to the unit cube tilings is given.
Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.
We have fundamentally corrected the proofs of the theorems from our paper [9] by giving an entirely different approach, using quite a simple method based on applications of some elementary inequalities, well-known H\"older's inequality, and…
In this article, we give a trajectorial proof of a kinetic Poincar\'e inequality which plays an important role in the De Giorgi-Nash-Moser theory for kinetic equations. The present work improves a result due to J. Guerand and C. Mouhot [10]…
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…