Bo-Yong Chen
We prove a sharp $L^p$ weighted Hardy inequality involving boundary distance $δ$ for any domain $Ω\subsetneq \mathbb R^n$. The inequality may be improved substantially under the additional assumption that $-\log δ$ is subharmonic. Applications of these inequalities to the principle frequency of the $p-$Laplacian are given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Some extensions of Hardy's integral inequalities to Hardy type spaces
本文将Hardy积分不等式推广到$0<p\leq 1$.
We prove fractional Sobolev-Poincaré inequalities, capacitary versions of fractional Poincaré inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results generalize and extend earlier work where such inequalities have been considered in the Euclidean spaces or in the non-fractional setting in metric spaces. The results concerning pointwise and localized variants of fractional Hardy inequalities are new even in the Euclidean case.
In between the inequalities of Sobolev and Hardy
本文建立了欧几里得空间开集上Hardy-Sobolev不等式成立的充分条件和必要条件。这些不等式在Sobolev不等式和Hardy不等式之间形成了一个自然的插值尺度。开集补集的Assouad维数在充分条件和必要条件中都起着重要的作用。
Hardy inequalities in Triebel-Lizorkin spaces II. Aikawa dimension
本文证明了域$G\subset\mathbb{R}^n$上Triebel-Lizorkin空间$F^s_{pq}(G)$中函数的Hardy型不等式，该域的边界具有严格小于$n-sp$的Aikawa维数.
A new approach to weighted Hardy-Rellich inequalities: improvements, symmetrization principle and symmetry breaking
本研究给出加权Hardy-Rellich不等式成立的权重充要条件，提出用Bessel对建立最优不等式的新方法，改进了已有结果，并部分解答了相关公开问题，明确了不等式对所有函数成立等价于对径向函数成立的权重条件。
In this paper, we prove the Hardy-Leray inequality and related inequalities in variable Lebesgue spaces. Our proof is based on a version of the Stein-Weiss inequality in variable Lebesgue spaces derived from two weight inequalities due to Melchiori and Pradolini. We also discuss an application of our results to establish an existence result for the degenerate $\pp$-Laplace operator.
Semilinear elliptic equations for the fractional Laplacian with Hardy potential
本文研究一类含Hardy位势的半线性分数阶椭圆型方程非负分布解的存在性和不存在性。
The effect of curvature in fractional Hardy--Sobolev inequality with the Spectral Dirichlet Laplacian
证明了具有边界奇异性的分数阶Hardy-Sobolev不等式中最佳常数的可达性。主要假设是原点处边界的平均曲率。
On the Sobolev and Hardy constants for the fractional Navier Laplacian
我们证明了在$\mathbb R^n$中的有界域上的Sobolev常数和Hardy常数相对于任何实阶$m\in(0,\frac{n}{2})$的“Dirichlet”和“Navier”分数拉普拉斯算子的重合性。
Improved Hardy and Rellich inequalities for antisymmetric and odd functions
本文研究了一般指数p下反对称与奇函数类的Hardy和Rellich不等式，得出了优于经典常数的改进结果。
Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups
在幂零李群的一个最一般的子群，即齐次群类上，给出了$L^{p}$的尖锐余项和加权Hardy和Rellich不等式.作为结果，我们得到类似的广义经典Hardy和Rellich不等式和不确定性原则齐次群。我们还证明了高阶Hardy-Rellich型不等式，所有尖锐的常数。一些身份推导出包括加权和更高的序型。
Geometric Hardy inequalities on starshaped sets
本文给出了卡诺群中星形集上的几何Hardy不等式。同时，我们得到了一般向量场在半空间上的几何Hardy不等式.
Local and global properties of minimal solutions for the heat equation generated by the Dirichlet fractional Laplacian negatively perturbed by Hardy's potentials on open subsets of $\R^d$ are analyzed. As a byproduct we obtain instantaneous blow-up of nonnegative solutions in the supercritical case.
In this paper we establish several Hardy and Hardy-Sobolev type inequalities with homogeneous weights on the first orthant $\displaystyle \mathbb{R}_{*}^n:=\{(x_1, \ldots, x_n):x_1>0, \ldots, x_n>0 \}$. We then use some of them to produce Hardy type inequalities with remainder terms. Furthermore, we obtain some interpolation inequalities and Maz'ya type inequalities with remainder terms with the help of Maz'ya inequality and Sobolev inequality of Cabré and Ros-Orton on the upper half space $\mathbb{R}_{+}^n:=\{x=(x_1, \ldots, x_n)|\, x_n>0 \}$.
Hardy Inequalities for the Heisenberg Laplacian on convex bounded polytopes
证明了第一Heisenberg群上开有界凸多胞体上Heisenberg Laplacian梯度的Hardy型不等式。Hardy不等式的积分权由到边界的距离函数给出，该距离函数相对于Carnot-Carathéodory度量测量。该常数取决于由凸多胞体的边界给出的与超平面$x_3=0$不正交的超平面的数量。
Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups
本文证明了一般齐次李群上的逆Stein-Weiss不等式。所得结果推广了以前已知的不等式。齐次范数的特殊性质和逆积分Hardy不等式在我们的证明中起着关键作用。同时，我们证明了齐次群上的逆Hardy，Hardy-Littlewood-Sobolev，Lp-Sobolev和Lp-Caffarelli-Kohn-Nirenberg不等式.
We construct new optimal $L^p$ Hardy-type inequalities for elliptic Schrödinger-type operators
We establish some qualitative properties of minimizers in the fractional Hardy--Sobolev inequalities of arbitrary order.
New Hardy type inequalities in sectorial area and as a limit in an exterior of a ball are proved. Sharpness of the inequalities is shown as well.
Hardy Inequalities in General Domains
关键词：Hardy不等式，Sobolev不等式，Morrey不等式，距离函数，中曲率，最佳常数，半凸，正可达集，平均凸集，Cheeger常数，连续模
This is the first part of our research on certain sharp Hardy-Sobolev inequalities and the related elliptic equations. In this part we shall establish some sharp weighted Hardy-Sobolev inequalities whose weights are distance functions to the boundary.
Signed and sign-changing solutions for a class Kirchhoff-type problem involving the fractional p-Laplacian with critical Hardy nonlinearity
本文研究了一类具有Sobolev和Hardy非线性项的非局部分数p-Laplacian算子的Kirchhoff方程在亚临界和临界增长下三个解的存在性.证明是基于山路定理、Ekeland变分原理和Nehari集上的约束极小化。
We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy type inequality derives both two Hardy type inequalities with best constants. Besides, we improve two Rellich type inequalities by using the improved Hardy type inequality.
Trace Hardy--Sobolev--Mazy'a inequalities for the half fractional Laplacian
本文对弱平均凸区域建立了具有最佳Hardy常数的迹Hardy-Sobolev-Maz'ya不等式.我们通过得到一个新的加权Hardy型估计来实现这一点。然后我们产生谱半拉普拉斯算子的Hardy-Sobolev-Maz'ya不等式。这涵盖了\cite{FMT1}中未解决的关键案例。
Though Adams and Hardy-Adams inequalities can be extended to general symmetric spaces of noncompact type fairly straightforwardly by following closely the systematic approach developed in our early works on real and complex hyperbolic spaces, higher order Poincaré-Sobolev and Hardy-Sobolev-Maz'ya inequalities are more difficult to establish. The main purpose of this goal is to establish the Poincaré-Sobolev and Hardy-Sobolev-Maz'ya inequalities on quaternionic hyperbolic spaces and the Cayley hyperbolic plane. A crucial part of our work is to establish appropriate factorization theorems on the…
In this article we prove both norm and modular Hardy inequalities for a class functions in one-dimensional fractional Orlicz-Sobolev spaces.
Hardy inequalities for general elliptic operators with improvements
我们得到了Hardy不等式的最优推广形式，作为特例，它包含Hardy不等式和涉及到$ Ω$边界的距离函数的Hardy不等式.此外，我们还得到了以非负势形式增加改进的必要和充分条件。
Sharp fractional Hardy inequalities with a remainder for $1<p<2$
本文研究了1<p<2范围内带有余项的分数Hardy不等式及其扩展形式
Hardy and Rellich inequalities for anisotropic p-sub-Laplacians
本文建立了次椭圆Picone型恒等式。作为结果，我们得到的Hardy和Rellich型不等式的各向异性p次拉普拉斯算子的形式$$ \mathcal{L}_p f := \sum_{i=1}^{N}X_i(|X_if|^{p_i-2}X_i f), \quad 1<p_i< \infty, $$其中$X_i, i=1,\ldots, N,$是一个分层（李）群的第一层的生成元。此外，在分层群上得到了多重奇点的Hardy型不等式和多粒子Hardy型不等式的类似结果.
Hardy Type Inequalities for $Δ_λ$-Laplacians
我们推导出一类属于$Δ_λ$ -Laplacian算子的子椭圆算子的Hardy型不等式，并找到了所涉及的常数的显式值.我们的结果推广了以前针对Grushin型算子$$ Δ_{x}+ |x|^{2α}Δ_{y},\qquad\ (x,y)\in\mathbb{R}^{N_1}\times\mathbb{R}^{N_2},\ α\geq 0, $$获得的不等式，这些不等式已被证明是尖锐的。
Bilinear Hardy inequalities on metric measure spaces
本文研究一般度量测度空间上的双线性Hardy不等式，刻画了具有极分解的度量测度空间中该不等式成立的权函数条件，并给出了其在齐次Lie群、双曲空间等空间上积分Hardy不等式的应用示例。
We introduce a geometric approach of integral curves for functional inequalities involving directional derivatives in the general context of differentiable manifolds that are equipped with a volume form. We focus on Hardy-type inequalities and the explicit optimal Hardy potentials that are induced by this method. We then apply the method to retrieve some known inequalities and establish some new ones.
Improved Multipolar Poincaré-Hardy inequalities on Cartan-Hadamard Manifolds
证明了Cartan-Hadamard流形上的一族改进的多极Poincaré-Hardy不等式。对于适当的极点配置，这些不等式得到了一个改进的多极Hardy不等式和一个改进的多极Poincaré不等式，使得在任意极点处都能达到临界单极奇异质量.
Weighted anisotropic Hardy and Rellich type inequalities for general vector fields
本文建立了一般（实值）向量场的带边界项的加权各向异性Hardy和Rellich型不等式.作为后果，我们得到新的以及许多基本的哈代和Rellich型不等式，这是已知的在不同的设置。
Hardy type inequalities with mixed weights in cones
本文研究锥体中带混合柱坐标与球坐标权重的Hardy型不等式，并揭示其与奇异或退化微分算子的关联。
Finsler Hardy inequalities
本文给出了在各种情况下各向异性Hardy不等式的一个统一的简单方法。我们考虑Hardy不等式，其中涉及Finsler距离从一个点或从一个域的边界。证明了不等式中常数的尖锐性和不可达性。
Anisotropic Hardy inequalities
研究了一类涉及$R^n$中的一般范数和到边界的各向异性距离函数的Hardy型不等式.常数的最优性的情况下也解决。
Fractional Hardy-Sobolev inequalities on half spaces
研究了半空间上包含s阶Dirichlet分数Laplacian（0<s<1）的Hardy-Sobolev不等式极值的存在性.
We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the existence/nonexistence of the extremal functions of the Hardy inequalities. These Hardy inequalities are in the spirit of Brezis-Vázquez in the Euclidean spaces. As direct consequences, we establish several Hardy type inequalities that provide substantial improvements as well as simple understandings to many known Hardy inequalities and Hardy-Poincaré-Sobolev type inequalities on hyperbolic spaces in the literature.
We give a sufficient condition for limiting Sobolev and Hardy inequalities to hold on stratified homogeneous groups. In the Euclidean case, this condition reduces to the known cancelling necessary and sufficient condition. We obtain in particular endpoint Korn--Sobolev and Korn--Hardy inequalities on stratified homogeneous groups.
$p$-Laplacian problems involving critical Hardy-Sobolev exponents
我们证明了存在性，多重性和分歧的结果$p$ -拉普拉斯问题涉及临界Hardy-Sobolev指数。我们的结果主要针对$λ\ge λ_1$情形，推广了文献中关于$0 < λ< λ_1$的结果.在没有直和分解的情况下，我们使用基于上同调指数和相关伪指数的临界点定理。
Sharp Hardy-Leray and Rellich-Leray inequalities for curl-free vector fields
本文证明了具有锐常数的无旋向量场的Hardy-Leray和Rellich-Leray不等式。这补充了Costin-Maz'ya \cite{Costin-Mazya}关于轴对称无发散向量场的Hardy-Leray不等式的工作。
The Brezis-Nirenberg problem for the fractional $p$-Laplacian involving critical Hardy-Sobolev exponents
我们得到了分数阶$p$ \nobreakdash -Laplacian算子Brezis-Nirenberg问题的存在性、多重性和分支结果，其中包含临界Hardy-Sobolev指数.我们的结果主要是文献中关于$α=0$的结果的推广。在分数Hardy-Sobolev不等式$α\not= 0$中的极小值的显式公式的情况下，我们通过最近在\cite{MM}中获得的极小值的某些渐近估计来解决这个困难。
On improved Hardy-type inequalities in Log-Weighted Sobolev Spaces
本文在对数加权Sobolev空间中证明尖锐Hardy型不等式，并通过添加最优余项实现无穷级数改进，进而得到最优Leray-Trudinger型改进及两类不等式间的插值。
Hardy and Hardy PDO type inequalities in domains. Part I
前面的“索伯列夫空间中的多项式容量、Poincare型不等式和谱综合“是本文的前提。推荐平行阅读。
Hardy inequalities for Robin Laplacians
本文建立了具有Robin边值条件的Laplace算子的Hardy不等式.对于凸区域，特别是，我们明确地显示了相应的Hardy重量取决于系数的罗宾边界条件。我们还研究了几个扩展到非凸和无界域。
The aim of this paper is to obtain new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. These inequalities give us the possibility to derive estimates from below of the first eigenvalue of the p-Laplacian with Dirichlet boundary conditions.
In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new estimates in miscellaneous situations, such as multipolar potential, the exponential weight, hyperbolic space, Heisenberg group, the edge Laplacian, or the Grushin type operator.
Firstly, this paper establishes useful forms of the remainder term of Hardy-type inequalities on general domains where the weights are functions of the distance to the boundary. For weakly mean convex domains we use the resulting identities to establish nonexistence of extremizers for and improve known sharp Hardy inequalities. Secondly, we establish geometrically interesting remainders for the Davies-Hardy-Tidblom inequalities for the mean distance function, as well as generalize and improve several Hardy type inequalities in the spirit of Brezis and Marcus and spectral estimates of Davies. L…
Extremal problem of Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds
利用集中紧原理研究了无边界紧致流形上Hardy-Littlewood-Sobolev不等式极值问题的存在性。
This paper is primarily devoted to a class of interpolation inequalities of Hardy and Rellich types on the Heisenberg group $\mathbb{H}^n$. Consequently, several weighted Hardy type, Heisenberg-Pauli-Weyl uncertainty principle and Hardy-Rellich type inqualities are established on $\mathbb{H}^n$. Moreover, new weighted Sobolev type embeddings are derived. Finally, an integral inequality for vector fields in a domain of the Heisenberg group is obtained, leading to several specific weighted Hardy type inequalities by making careful choices of vector fields.
Hardy-type inequalities for vector fields with the tangential components vanishing
本文研究了$\curl$的$L^1$范数下的向量场的Hardy型不等式.与全空间中关于无散度向量的著名结果不同，我们将Hardy型不等式推广到有界域和边界切向分量为零的非无散度向量场.
Application of Hardy inequalities for some singular parabolic equations
本文研究具有奇异势的非线性抛物型方程边值问题，利用不同Hardy不等式证明了存在性与不存在性结果，并探讨了爆破条件。
Hardy inequalities with homogenuous weights
本文得到了单位球面上允许奇点的几个带权函数的Hardy不等式.为了证明本文的主要结果，我们利用文献[DEL]中关于单位球面上Schr dinger算子最低本征值的一些新的尖锐不等式.
We present a unified strategy to derive Hardy-Poincaré inequalities on bounded and unbounded domains. The approach allows proving a general Hardy-Poincaré inequality from which the classical Poincaré and Hardy inequalities immediately follow. The idea also applies to the more general context of variable exponent Sobolev spaces. The argument, concise and constructive, does not require a priori knowledge of compactness results and retrieves geometric information on the best constants.
Hardy inequalities, Rellich inequalities and local Dirichlet forms
首先，Hardy和Rellich不等式的定义与局部Dirichlet形式的submarkovian算子。其次，给出了由Hardy不等式导出Rellich不等式的两个一般条件。此外，Rellich常数由Hardy常数计算。第三，我们建立了区域$Ω\subseteq \Ri^d$上一类二阶加权算子的Rellich不等式的判别准则。边界附近的加权$\partial Ω$可以不同于无穷远处的加权。最后将这些结果应用于$\Ri^d\backslash\{0\}$上的加权二阶算子和一类一般的Grushin型算子。
On fractional Orlicz boundary Hardy inequalities
本文研究有界Lipschitz域上的分数阶Orlicz边界Hardy型不等式，并在多类域中对特定临界情形建立了带对数修正的不等式。
For the fractional Laplacian we give Hardy inequality which is optimal in $L^p$ for $1<p<\infty$. As an application, we explicitly characterize the contractivity of the corresponding Feynman-Kac semigroups on $L^p$.
We establish sharp two-sided bounds on the heat kernel of the fractional Laplacian, perturbed by a drift having critical-order singularity, by transferring it to appropriate weighted space with singular weight.
Corrigenda to "$L^p$ estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities", Trans. Amer. Math. Soc. 363 (2011), no. 1, 37--62.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。