相关论文: Generalized Polya-szego Inequality
We prove a Lojasiewicz-Simon inequality $$ \left| E(u) - 4\pi n \right| \leq C \| \mathcal{T}(u) \|^\alpha $$ for maps $u \in W^{2,2}\left( S^2, S^2 \right).$ The inequality holds with $\alpha = 1$ in general and with $\alpha > 1$ unless…
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
We prove higher integrability of the spatial gradient of weak solutions to parabolic systems with $\phi$-growth, where $\varphi=\varphi(t)$ is a general Orlicz function. The parabolic systems need be neither degenerate nor singular. Our…
A basic version of the P\'olya-Szeg\H{o} inequality states that if $\Phi$ is a Young function, the $\Phi$-Dirichlet energy -- the integral of $\Phi(\|\nabla f\|)$ -- of a suitable function $f\in \mathcal{V}(\mathbb{R}^n)$, the class of…
In this paper, we construct a new integrable equation which is a generalization of $q$-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the generalized $q$-Toda…
Necessary and sufficient conditions are exhibited for a Korn type inequality to hold between (possibly different) Orlicz norms of the gradient of vector-valued functions and of the deviatoric part of their symmetric gradients. As a…
Let H be the supremum of finitely many real polynomials of degree d and assume that H has a strict local minimum at 0. We prove a \L ojasiewicz-type inequality $H(x_1,...,x_n) > ||(x_1,...,x_n)||^s$ where s depends only on d and n. This…
A generalized Bogomolov-Gieseker inequality for tilt-stable complexes on a smooth projective threefold was conjectured by Bayer, Toda, and the author. We show that such inequality holds true in general, if it holds true when the…
In this paper, we first prove the Hardy-Sobolev inequality for the Hessian integral by means of a descent gradient flow of certain Hessian functionals. As an application, we study the existence and regularity results of solutions to related…
This preprint is a text for students and teachers on inequalities. Some standard topics are covered on application of calculus to inequality proving. Many examples are considered, stated, solved or partially solved. Some problems are…
In this work, a generalization of Chebyshev functional is presented. New inequalities of Gruss type via Pompeiu's mean value theorem are established. Improvements of some old inequalities are proved. A generalization of pre-Gruss inequality…
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
The Paouris inequality gives the large deviation estimate for Euclidean norms of log-concave vectors. We present a modified version of it and show how the new inequality may be applied to derive tail estimates of l_r-norms and suprema of…
We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Bj\"orner--Wachs inequality and generalize it to inequalities on order polynomials and their $q$-analogues via direct…
In this paper, we introduce and prove the generalizations of Radon inequality. The proofs in the paper unify and are simpler than those in former work. Meanwhile, we also find mathematical equivalences among the Bernoulli inequality, the…
Some inequalities for functions of bounded variation that provide reverses for the inequality between the integral mean and the p-norm are established. Applications related to the celebrated Landau inequality between the norms of the…
We prove inequalities involving greatest common divisors of functions at integral points with respect to numerically parallel divisors, generalizing a result of Wang and Yasufuku (after work of Bugeaud-Corvaja-Zannier, Corvaja-Zannier, and…
We prove a weak-strong convergence result for functionals of the form $\int_{\mathbb{R}^N} j(x, u, Du)\,dx$ on $W^{1,p}$, along equiintegrable sequences. We will then use it to study cases of equality in the extended Polya-Szeg\"o…
We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations
We prove a parabolic version of the Littlewood-Paley inequality for the fractional Laplacian $(-\Delta)^{\alpha/2}$, where $\alpha\in (0,2)$.