查询词典 sobolev space

In general L_p spaces,one can characterize the smoothness of refinement function with Lipschitz space. In particular, one can characterize the smoothness of refinement function in Sobolev spaces.

对于一般的L_p空间，在细分方程收敛的前提下，对细分函数光滑性的刻画用一般的Lipschitz空间即可；特别地，当p=2时，可以在Sobolev空间中去刻画其光滑性。

Second order differential inclusion; boundary condition; usc multivalued map; fixed point; monotone map; Yosida approximation; solution tube; upper-lower solutions; critical point; PS-condition; C-condition; Sobolev space

基础科学，数学，数学分析二阶微分包含；集值边界；上半连续集值映照；不动点；单调算子； Yosida逼近；解管道；上下解；临界点； PS-条件； C-条件； Sobolev空间

Are also given by constructing Lyapunov function. Finally, by applying the energy methods, Sobolev embedding theorems and bootstrap arguments, the global existence of nonnegative classical solutions to equations with homogeneous Neumann boundary value condition is proved when the space dimension is at most 5. Under certain conditions for the coefficients of the reaction functions, the convergence of the solutions is established for the system with large diffusion coefficients by constructing Lyapunov function.

的正平衡点全局渐近稳定的充分条件；最后，当空间维数不超过5时，应用能量估计、Sobolev嵌入定理和bootstrap技巧证明在齐次Neumann边值条件下非负古典解的整体存在性，并通过构造Lyapunov函数给出当反应函数的系数满足一定条件、扩散系数较大时该模型解的收敛性。

Since the solutions of this problem are the critical points of the associated energy function. One generally needs some compactness such as PScondition or C-condition to prove the existence of critical points of the energy func-tion, but when we study the elliptic equation in R~N, the compactness condition does not always hold since the imbedding of the Sobolev space H_0~(1,2)into L~(2*) is not compact. In this chapter, based on the nonsmooth critical point theory, and by using the approximation technique with periodic function, the existence of nontrivial solution is obtained.

由于该方程的解就是其所对应的能量泛函的临界点，通常都要在一些紧型条件的基础上来证明其所对应的能量泛函临界点的存在性，但当我们在无界域上考虑该椭圆方程解的存在性时，Sobolev空间H_0~(1，2)到L~(2*)的嵌入非紧，从而导致所对应的能量泛函失去紧性，本章在非光滑临界点理论的基础上，应用周期逼近的方法证明该问题非平凡解的存在性。

And for multi-dimension the conditions of the problems with sufficiently regular and star-shaped domain are also given, which have no solutions in Sobolev space.

给出了在空间维数为一时所论问题有无界解的条件，以及在高维空间时，区域充分规则和星形情形下，所论边值问题在Sobolev空间无解的条件。

2The new cloud physical model is put forward the metric geometry.(3)The generalized cloud equations of cloud is derived on the generalized function and the Sobolev space on the Riemannian manifold.

提出了 大气模式中新一代云方案的动力学：(1)基于拓扑的云分类；(2)基于度量几何的云模型(3)利用黎曼流型上的广义函数和索伯列夫空间，系统建立了云之动力学方程组。

The necessarity and sufficiency condition of weakly sequential semicontinuity for variational integrals are obtained in the setting of Orlicz-Sobolev space, which generalizes the corresponding results for variational problems with polynomial growth.

研究了非多项式增长的变分泛函，利用Orlicz空间理论，得到了其在Orlicz-Sobolev空间中弱序列下半连续的充要条件，推广了关于多项式增长的变分泛函的相应结论。

Through studing the weak solution in Sobolev space,its solvability has been proved.

通过在Sobolev 空间中对弱解的讨论，证明了它的可解性。

Moreover, we will stress on the theory of Schwartz distribution, and then we will deal with the celebrating theory which we call Sobolev space.

进一步，我们将讲授Schwartz广义函数基本理论，在此基础上我们讲授Sobolev空间的基本理论。

Keywords Sobolev space;generalized function;Galerkin method;nonlinear elastic bar;existence and uniqueness of solution

Sobolev空间；广义函数； Galerkin法；非线性弹性杆；解的存在性和唯一性

Article 144 The Government of the Hong Kong Special Administrative Region shall maintain the policy previously practised in Hong Kong in respect of subventions for non-governmental organizations in fields such as education, medicine and health, culture, art, recreation, sports, social welfare and social

第一百四十四条香港特别行政区政府保持原在香港实行的对教育、医疗卫生、文化、艺术、康乐、体育、社会福利、社会工作等方面的民间团体机构的资助政策。原在香港各资助机构任职的人员均可根据原有制度继续受聘。

Small wonder, then, that the Chinese spend more in the shop than any other group of foreign visitors do .

这样的小惊喜，使中国顾客比任何国家的人消费得更多。