Hardy 不等式: 设p>1,an为非负数列 ∑n=1∞∑k=1nakn≤(pp−1)p∑n=1∞anp 证明&分析 对于p>1证明似乎没有任何思路,不妨取一个个例来证明,毕竟 个性包含共性,共性寓于个性 取p=2因为这是满足条件最小的整数 即∑n=1∞(a1+...+ann)2≤4∑n=1∞an2一个平方小于另一个平方,容易联想到柯西...
詹森不等式 f 是区间上的下凸函数,对于任意的 x_i 和正数 λ_i (满足 ∑λ_i=1 ),有 f(∑λ_ix_i)≤∑λ_if(x_i) 。柯西-施瓦兹 不等式(Cauchy-Schwarz Inequality)设 x = (x_1, x_2,… 暴龙兽 Bellman-Gronwall不等式的推广命题 两只猫 分析中三个常用不等式——Young、Holder、Minkowski不...
1)Hardy inequalityHardy不等式 1.The fundamental solution andHardy inequalityfor 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 investig...
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。
A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics 2002, Archive for Rational Mechanics and Analysis Sobolev versus hölder local minimizers and global multiplicity for some quasilinear elliptic equations 2000, Communications in Contemporary Mathematics Multip...
A Hardy inequality of the form ∫Ω | ∇ f ( x ) | p d x ⩾ ( p − 1 p ) p ∫Ω { 1 + a ( δ , ∂ Ω ) ( x ) } | f ( x ) | p δ ( x ) p d x , for all f ∈ C 0 ∞ ( Ω ∖ R ( Ω ) ) , is considered for p ∈ ( 1 , ∞ ) , ...
An integral inequality of the following type and its modifications are called to be of the Hardy-type (1)[∫Ω |u(x)| q w(x)dx] 1/q ≤C{∑ i=1 N ∫Ω |u(x)/x i | p v i (x)dx} 1/p , where Ω is a domain in the N- dimensional Euclidean space; C, q, and p≥...
1. Introduction The classical Hardy inequality reads as follows ∞ 0 |u(x)| p x −p+a dx ≤ p p −1 −a p ∞ 0 |u (x)| p x a dx, where 1 < p < ∞, a < p − 1, u is absolutely continuous on [0, ∞), and u(0) = 0. It seems that the first to ...
A Hardy inequality of the form ∫Ω | f ( x ) | p d x ( p 1 p ) p ∫Ω { 1 + a ( δ , Ω ) ( x ) } | f ( x ) | p δ ( x ) p d x , for all f ∈ C 0 ∞ ( Ω R ( Ω ) ), is considered for p ∈ ( 1 , ∞ ), where Ω is a domain in R...
p.可以参考：https://math.stackexchange.com/questions/358861/hilberts-inequality