1) Hardy type inequality
Hardy型不等式
1.
The Hardy type inequality is extended to the Banach-space-valued Vilenkin martingales-Fourier coefficients.
对Banach空间值Vilenkin鞅建立了Hardy型不等式,推广了Weisz中的相应结论。
2.
A class of Hardy type inequality is given by the method of function representation and the method of Picone indentity on Rn.
先用函数表示和Picone恒等式的方法建立高维欧氏空间的一类Hardy型不等式,结合CAFFARELLI、KOHN、NIRENBERG三人证明Caffarelli-Kohn-Nirenberg不等式的思想,给出Caffarelli-Kohn-Nirenberg不等式的证明,突破原文需转化为一维情形的限制,对高维空间的情形直接证明,易于推广。
3.
The best constant in the Hardy type inequality for the sub-Laplacian is determined.
文章得到了Heisenberg型群上的几类Hardy型不等式,并确定出了次Laplace算子的Hardy型不等式中的最佳常数。
2) Hardy-type inequality
Hardy型不等式
1.
Then we give the estimate of the fundamental eigenvalue ratio,using the Hardy-type inequality on the bounded domain.
运用Ljusternik-Schnirelman原理,我们给出了特征值序列的存在性,然后利用有界域上的Hardy型不等式,给出了基本特征值率的估计。
3) improved Hardy inequality
改进型Hardy不等式
1.
By using the improved Hardy inequality and variational methods, we discuss the positive solutions of the elliptic boundary value problem -△u-μu/|x|2=u2*-1+f(x, u),whereΩ(?)RN is a smooth bounded domain such that 0∈Ω,andμ∈R is a parameter.
应用改进型Hardy不等式和变分方法,讨论了一类椭圆边值问题的正解:-△u-μu/|x|2=u2*-1+f(x, u),u∈H0 1(Ω),其中Ω是RN(N≥3)中包含的0有界光滑区域,μ∈R是一个参数。
2.
By using the improved Hardy inequality and the strong maximum principle,combining the sub-supersolution method and the mountain pass lemma,we obtain the existence results of multiple positive solutions under certain conditions.
讨论一类具Hardy位势的奇异拟线性椭圆方程,应用改进型Hardy不等式和强极大值原理,并结合上下解方法与山路引理证明了方程在适当条件下多重正解的存在性。
4) Hardy-Hilbert type inequality
Hardy-Hilbert型不等式
1.
By obtaining an inequality of the weight coefficient,a strengthened Hardy-Hilbert type inequality and its dual form are established.
求出了一个权系数的不等式,建立了一个Hardy-Hilbert型不等式及其对偶式的加强式,并考虑了其等价式的加强形式。
5) Hardy-type integral inequality
Hardy型积分不等式
1.
By introducing parameters a and b,and using the way of weight function,we give some extensions of a Hardy-type integral inequality and prove that the constant factors in some extended inequalities are the best possible.
引入参数a,b(0
2.
By introducing parameters a and b, and using the way of weight function, we give some generalizations of the Hardy-type integral inequality and prove that the constant factors in some extended inequalities are the best possible.
引入参数a,b,应用权函数的方法,建立Hardy型积分不等式的若干推广式,并证明某些推广式的常数因子是最佳的。
3.
By applying the way of weight function,a multiple Hardy-type integral inequality is given and its constant factor is the best possible is proved.
应用权函数方法,将一类Hardy型积分不等式推广到多重积分形式,并证明其中的常数因子是最佳的。
6) Hardy inequality
Hardy不等式
1.
The fundamental solution and Hardy inequality for a class of degenerated elliptics operators with a double-weight;
一类双权退化椭圆算子的基本解及Hardy不等式
2.
In this paper,the existence of the nontrivial solution to a class of quasi-linear elliptic problem is investigated based on the Hardy inequality and the Mountain Pass Geometry.
使用Hardy不等式和山路几何研究了一类拟线性椭圆问题非平凡解的存在性。
3.
This paper discusses a class special elliptic equation with strong singular item and critical Sobolev exponents by Variational method in PDE and Hardy inequality.
运用变分方法及Hardy不等式讨论了一类特殊的椭圆方程,证明了在一定条件下方程解的存在性。
补充资料：Hardy不等式
Hardy不等式
Hardy inequality
吵理报彝砂否料黯”‘’‘”-矛「玉1，，「一1，于。， ”目Ln」LP一l」，二，‘’ 其中a。不全等于零.在这个不等式中，常数(p/(p一 l))p是最佳的. 2)羊丁移分的Ha[dy不等术: )一…介(!)‘!…’J二〔司’i，了‘·，，一 P>l， 和 1 Ji，(!)Jt…’J一i，·“·，，’“一‘·对于使不等式左端为有限的一切函数，这两个不等式成立，只是f(义)在(O，十的)上几乎处处为零的情况除外.(在这种情况下，不等式变为等式).常数(P/(夕一l)户)和vp是最佳的. Ha川y积分不等式可以推广到任意区间:引一夕〔!)J!}’己…i，二了‘·，，，己一’一告，引一i，(!)‘!…’/二i，二了(·，，”dx，一告，其中O(a
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条