Hardy-Sobolev inequality with higher dimensional singularityExistence of ground state solutionHardy-Sobolev inequalityscalar curvaturesubmanifoldmean curvatureFor N ≥ 4, we let Ω be a smooth bounded domain of R~N, T a smooth closed submanifold of Ω of dimension k, with 1 ≤ k ≤ N - 2, ...
俄罗斯数学家最近证明了一个重要的数学不等式。这个成果具有重要的数学和物理学意义。所提供的新的数学工具可以大大简化量子力学和其他物理领域的计算。该研究成果发表在最近的《数学札记》杂志上。 这个数学不等式的名字叫哈代–利特伍德–索博列夫不等式(Hardy-Littlewood-Sobolev inequality,简称HLS不等式)。下面我们尽量...
This has a natural place with the Hardy and Sobolev inequalities as the three inequalities are intimately related, as we shall show. Where proofs are omitted, e.g., of the Sobolev inequality, precise references are given, but in all cases we have striven to include enough background ...
摘要: The attainability of the exact constant in the Hardy-Sobolev inequality is established in an arbitrary cone in n . Bibliography: 17 titles.关键词: CiteSeerX citations Hardy-Sobolev Inequalities in a cone A I Nazarov DOI: 10.1007/s10958-005-0508-1 ...
inequality in [ 37 ]. because of the drift, the class of operators we study has infinitely many pseudometrics driving the evolution, there is in general no doubling condition for the volume function, and there is no natural “gradient” associated. let us mention the few sobolev-type ...
SobolevinequalitywithnegativepowerbyW.Chen,etal.[5],YangandZhu[34],Hangand Yang[18],NiandZhu[31–33],Hang[16],etc.westartedtoinvestigatethegeneralextension ofHardy–Littlewood–Sobolev(HLS)inequality.InDouandZhu[8],weestablishedtheHLS inequalityontheupperhalfspace,andoutlinedtheroughideaontheextension...
We obtain the sharp constant for the Hardy-Sobolev inequality involving the distance to the origin. This inequality is equivalent to a limiting Caffarelli... Adimurthi,S Filippas,A Tertikas - 《Nonlinear Analysis Theory Methods & Applications》 被引量: 122发表: 2009年 Inequalities of Hardy–Sobo...
Hardy–Littlewood–Sobolev inequality42B3542B2542B10We introduce the Riesz potential associated with the Weinstein operator of order s , as where is its heat semigroup. Next, we define the fractional Littlewood–Paley g -function denoted of order s , as where is the Poisson integral of f . ...
This has a natural place with the Hardy and Sobolev inequalities as the three inequalities are intimately related, as we shall show. Where proofs are omitted, e.g., of the Sobolev inequality, precise references are given, but in all cases we have striven to include enough background ...
其中,=f1是(1)成立的最好常数.[2]得到如下改进型Hardy—Sobolev不等式 J^-Vu≥()nl+C』nl)～ 其中N≥eZ/?supll,"∈w(n).在本文,我们将对(2)中的常数C进行研究,并给出该 常数的一个上界.为了对(2)中常数C进行估计,我们引进几个记号并给出有关的引 ...