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排序方式: 共有112条查询结果,搜索用时 29 毫秒
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In this article, we have two parts. In the first part, we are concerned with the locally Hlder continuity of quasi-minima of the following integral functional ∫Ωf(x, u, Du)dx, (1) where Ω is an open subset of Euclidean N-space (N ≥ 3), u:Ω→ R,the Carath′eodory function f satisfies the critical Sobolev exponent growth condition |Du|p* |u|p*-a(x) ≤ f(x,u,Du) ≤ L(|Du|p+|u|p* + a(x)), (2) where L≥1, 1pN,p* = Np/N-p , and a(x) is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally Hlder continuity of ω-minima of (1). Our method is to compare the ω-minima of (1) with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland’s variational principal. 相似文献
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Yuxi ZHENG 《数学年刊B辑(英文版)》2009,30(6):845-858
Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult, but a viable alternative remains missing. The author lists merits of one-dimensional Riemann problems and compares them with those for the current two-dimensional Riemann problems, to illustrate their worthiness. Two-dimensional Riemann problems are approached via the methodology promoted by Andy Majda in the spirits of modern applied mathematics; that is, simplified model is built via asymptotic analysis, numerical simulation and theoretical analysis. A simplified model called the pressure gradient system is derived from the full Euler system via an asymptotic process. State-of-the-art numerical methods in numerical simulations are used to discern smallscale structures of the solutions, e.g., semi-hyperbolic patches. Analytical methods are used to establish the validity of the structure revealed in the numerical simulation. The entire process, used in many of Majda's programs, is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws 相似文献
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定光桂 《数学物理学报(B辑英文版)》2009,29(3):469-479
This is such a article to consider an "into" isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition (using the Krein-Milman property) under which an into-isometric mapping from the unit sphere of e(Γ) to the unit sphere of a normed space E can be linearly isometric extended. 相似文献
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高维空间的拟正则映照 总被引:1,自引:0,他引:1
1引言 众所周知,设Ω是一个复平面区域,则中的Beltrami方程:的解w=f(z)称为上的 正则函数,当w=f(z)是同胚的时候,称为 共形映照.正则函数和什共形映照在复分析中有重要的理论意义和广泛的应用,并已被深入系统的研究[1-5].如何将它们推广到高维长期受到人们的关注,并已有了一些重要的工作.最近T.Iwaniec和G.Martin得到了Beltrami方程和正则函数的正则性理论在偶数维空间中的相应推广,这是拟正则函数的正则性理论研究中的一个重要发展[6];之后T.Iwaniec应用变… 相似文献
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In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights making use of multivariate decompose skills and results of one-dimensional Baskakov operators, and obtain the direct approximationtheorem. 相似文献
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二维锌枝晶生长行为研究 总被引:9,自引:0,他引:9
采用恒电压方法得到了不同电解质浓度和电压下金属锌二维电沉积生长的形貌分布图.在枝晶生长条件下,研究了支持电解质、全氟表面活性剂和脉冲电压等对锌枝晶生长行为的影响,并检测了电解池中Zn^2 的浓度分布.实验结果表明:支持电解质、表面活性剂和脉冲电压改变了阴极附近的电场分布和Zn^2 的浓度分布,对沉积物形貌产生很大的影响.同时发现,Zn^2 仅通过电迁移作用到达阴极附近,扩散对传质的贡献可忽略不计. 相似文献
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本文对一类有广泛应用价值的不规则的条件泛函极值问题的解的存在性及解的解析表示式进行了深入系统的讨论,得到了一系列在理论及应用上颇有价值的结果.对该类问题最优解的存在性的证明填补了这方面的空白. 相似文献
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1 INTRODUCTION Metalloporphyrins and their derivatives having been intensively studied play an important role in biological processes, such as oxygen transport and photosynthesis. They can act as catalysts[1] and un- dergo reversible redox reactions in which the site of electron transfer may be localized on the porphyrin ring or the central metal ion. Both reactions are important in natural processes[2]. Recently, it hasbecome known that structural distortion from planar geometry is fairl… 相似文献