1) Sobolev space norm
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Sobolev空间范数
2) negative Hilbert-Sobolev space
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负指数Hilbert-Sobolev空间
3) variable exponent Sobolev space
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变指数Sobolev空间
4) Variable exponent Sobolev spaces
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变指数Sobolev空间
1.
With some symmetry assumptions and growth conditions on nonlinearities, the existences of infinitely many solutions are obtained by using a limit index theory developed by Li (Nonlinear Analysis: TMA, 25(1995) 1371-1389) in variable exponent Sobolev spaces W_0~(1,p(x)(Ω) and W_1~(1,p(x)(R~N) respectively.
在对非线性项作适当对称性假设和增长性条件后,我们分别在变指数Sobolev空间W_0~(1,p(x))(Ω)和W~(1,p(x))(R~N)中,利用极限指标理论(Nonlinear Analysis:TMA,25(1995)1371-1389)得到了两类方程组的无穷多解性。
2.
In this paper, we consider differential inclusion problem in a bounded domainΩ, involving p(x)-Laplacian of Neumann-typeand Dirichlet-typeWith some suitable assumptions on nonlinearities, the existences of infinitely many solutions are obtained by using nonsmooth version Ricceri\'s variational principle in variable exponent Sobolev spaces W~(1,(p(x)))(Ω) and W_0~(1,(p(x)))(Ω), respectively.
在这篇文章中,我们在有界域Ω上分别考虑了包含p(x)-Laplacian算子的Neumann型的微分包含问题和Dirichlet型的微分包含问题在对非线性项作适当假设后,我们分别在变指数Sobolev空间W~(1,(p(x)))(Ω)和W_0~(1,(p(x)))(Ω)中,利用非光滑型Ricceri变分原理得到了两类问题的无穷多解性。
3.
Ric-ceri (Nonlinear Analysis 70(2009) 3084-3089) in variable exponent Sobolev spaces W_0~(1,p(x))(Ω)×W_0~(1,q(x)(Ω).
在p(x),q(x)与N不同的大小关系下,对非线性项做适当假设和增长性条件,我们在变指数Sobolev空间W_0~(1,p(x))(Ω)×W_0~(1,(q(x))(Ω)中,利用Ricceri三临界点定理(Nonlinear Analysis 70(2009)3084-3089)得同一方程组在不同条件下的三解性。
5) variable exponent Lebesgue-Sobolev spaces
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变指数Lebesgue-Sobolev空间
6) Hilbert-Sobolev norm
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Hilbert-Sobolev范数
1.
Firstly, through applying Hilbert-Sobolev norm to measure fidelity term, a total variation filter is used to smooth the normal vectors of the level curves of a noise image.
该方法首先引入负指数Hilbert-Sobolev范数度量逼近项,对图像水平曲线的法向量场进行全变差正则化磨光,然后构造出一个曲面拟合模型,拟合磨光后的流场。
补充资料:可数赋范空间
可数赋范空间
oountabiy-oormed space
可数斌范空间「。晚.扭街一~曰月班理;创曰旧侧明州阅,-.砚旧。旧即以汀脚川。BOI 由担夸苹攀(“〕m脚tlble noITns,}}。卜、,…,{,{{。,…的可数集来定义其拓扑的局部凸空间,这里!*}},与!{*!}、相容是指如果序列{戈}CX是按这两个范数的基本序列,且按其中一个范数趋于零,那么它也按另一个范数趋于零.范数序列{}}*{一}可由非减范数序列(即当p
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