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应用对合变换建立了两类变量的经典变分原理———Hamilton原理 .灵活应用Lagrange乘子法 ,建立了完整系统和非完整系统的两类变量的广义变分原理和带有附加条件的广义变分原理 .推导了各类变分原理的驻值条件. 相似文献
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A-调和方程很弱解的正则性 总被引:8,自引:0,他引:8
本文证明了二阶拟线性偏微分方程很弱解的正则性.若u是(1)的一个很弱解并属于一个合适的包含W1,p loc( )的空间,则u属于 ( ),即u是(1)通常意义下的弱解.变分积分弱极值的同样结果被得到. 相似文献
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与A-调和方程有关的两个结果 总被引:2,自引:0,他引:2
给出两个与A 调和方程有关的结果 .第一个结果是一类A 调和方程的很弱解可由调和函数逼近 .另一个是变分积分弱极值的充分必要条件 相似文献
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本文讨论在结构力学中用拉格朗日乘子法建立的广义变分原理以分析非线性超静定结构。我们假定结构的材料关于应力-应变的关系具有σ=Bε1/m或τ=Cγ1/m的形式,即结构的物理方程具有幂函数的形式。文中举出几个超静定结构的例子,例如桁架、梁、刚架和扭杆。 相似文献
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自从钱伟长建立了功率型变分原理以来,功率型变分原理和功能型变分原理在理论方面和应用方面有什么区别和联系,成为学术界关注的课题.应用变积方法,根据Jourdain原理和d’Alembert原理,建立了不可压缩黏性流体力学的功率型变分原理和功能型拟变分原理,推导了不可压缩黏性流体力学的功率型变分原理的驻值条件和功能型拟变分原理的拟驻值条件.研究了不可压缩黏性流体力学的功率型变分原理在有限元素法中的应用.研究表明,功率型变分原理与Jourdain原理相吻合,功能型变分原理与d’Alembert原理相吻合.功率型变分原理直接在状态空间中研究问题,不仅在建立变分原理的过程中可以省略在时域空间中的一些变换,而且给动力学问题有限元素法的数值建模带来方便. 相似文献
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入水冲击问题变分原理及其它 总被引:3,自引:0,他引:3
首先建立入水前后两个衔接阶段的较为严密的场方程.再得到与之对应的各类变分原理,界限定理,第二阶段问题的边界积分方程.证明了解的存在性并提供了求解实施方案.最后以船舶兴波阻力问题的算例,论证了第二阶段问题的一种特殊应用及其正确性.从而为求取较为精确的入水冲击问题基本方程的变分有限元及边界元方法奠定了严密的理论基础. 相似文献
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本文发现,弹性力学中的胡-鹫津三类变量广义变分原理在作了一些细小的修改后可以化为max min max min原理。根据这个原理,本文建立了用Ritz法能得到能量上合理的近似解的充要条件(本文第四节表2中的4个条件)。 相似文献
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本文给出了Banach空间广义分解定理的一个初等证明,并利用它来证明两个对称不等式.这是首次在Banach空间获得这样的不等式. 相似文献
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Lise‐Marie Imbert‐Gérard Leslie Greengard 《Numerical Methods for Partial Differential Equations》2017,33(3):941-955
The inversion of the Laplace‐Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many areas of science, from computer graphics to machine learning to computational physics. Here, we present a high‐order accurate pseudo‐spectral approach, applicable to closed surfaces of genus one in three‐dimensional space, with a view toward applications in plasma physics and fluid dynamics. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 941–955, 2017 相似文献
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Faran posed an open problem about analysis on complex Finsler spaces: Is there an analogue of the (θ)-Laplacian? Is there an analogue of Hodge theory? Under the assumption that (M, F) is a compact strongly K(a)hler Finsler manifold, we define a (θ)-Laplacian on the base manifold. Our result shows that the well-known Hodge decomposition theorem in K(a)hler manifolds is still true in the more general compact strongly K(a)hler Finsler manifolds. 相似文献
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De Rham Cohomology and Hodge Decomposition For Quantum Groups 总被引:1,自引:0,他引:1
Let be one of the N2-dimensionalbicovariant first order differential calculi for the quantumgroups GLq(N), SLq(N), SOq(N), or Spq(N), where q is a transcendentalcomplex number and z is a regular parameter. It is shown thatthe de Rham cohomology of Woronowicz' external algebra coincides with the de Rham cohomologiesof its left-coinvariant, its right-coinvariant and its (two-sided)coinvariant subcomplexes. In the cases GLq(N) and SLq(N) thecohomology ring is isomorphic to the coinvariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in thesecases. The main technical tool is the spectral decompositionof the quantum Laplace-Beltrami operator. 2000 MathematicalSubject Classification: 46L87, 58A12, 81R50. 相似文献
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By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the notion of infinitesimal
variation of Hodge structure at infinity is introduced. It is shown that all such structures can be integrated to polarized
variations of Hodge structure and that, conversely, all are limits of infinitesimal variations of Hodge structure at finite
points. As an illustration of the rich information encoded in this new structure, some instances of the maximal dimension
problem for this type of infinitesimal variation are presented and contrasted with the “classical” case of IVHS at finite
points.
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Hossein Movasati 《Bulletin of the Brazilian Mathematical Society》2008,39(1):81-107
Around 1970 Griffiths introduced the moduli of polarized Hodge structures/ the period domain D and described a dream to enlarge D to a moduli space of degenerating polarized Hodge structures. Since in general D is not a Hermitian symmetric domain, he asked for the existence of a certain automorphic cohomology theory for D, generalizing the usual notion of automorphic forms on symmetric Hermitian domains. Since then there have been many efforts
in the first part of Griffith's dream but the second part still lives in darkness. The objective of the present text is two-folded.
First, we give an exposition of the subject. Second, we give another formulation of the Griffiths problem, based on the classical
Weierstrass uniformization theorem. 相似文献
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José Alberto Montero 《Journal of Functional Analysis》2008,254(7):1926-1973
We solve a Hodge decomposition problem with respect to a weight function that vanishes on the boundary. This problem is present in several works on the Gross-Pitaevskii energy, and we use our solution to show that a Γ-convergence result that links these works is still valid for more general data than previously considered. 相似文献
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ZHONG Chunping & ZHONG Tongde School of Mathematical Sciences Xiamen University Xiamen China Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2006,(11)
Faran posed an open problem about analysis on complex Finsler spaces: Is there an analogue of the (?)-Laplacian? Is there an analogue of Hodge theory? Under the assumption that (M,F) is a compact strongly Kahler Finsler manifold, we define a (?)-Laplacian on the base manifold. Our result shows that the well-known Hodge decomposition theorem in Kahler manifolds is still true in the more general compact strongly Kahler Finsler manifolds. 相似文献
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We present a survey of the properties of the monodromy of local systems on quasi-projective varieties which underlie a variation of Hodge structure. In the last section, a less widely known version of a Noether–Lefschetz-type theorem is discussed. 相似文献
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A. Ern J.‐L. Guermond L. Quartapelle 《Mathematical Methods in the Applied Sciences》1999,22(6):531-546
This work studies the three‐dimensional Stokes problem expressed in terms of vorticity and velocity variables. We make general assumptions on the regularity and the topological structure of the flow domain: the boundary is Lipschitz and possibly non‐connected and the flow domain may be multiply connected. Upon introducing a new variational space for the vorticity, five weak formulations of the Stokes problem are obtained. All the formulations are shown to lead to well‐posed problems and to be equivalent to the primitive variable formulation. The various formulations are discussed by interpreting the test functions for the vorticity (resp. velocity) equation as vector potentials for the velocity (resp. vorticity). Of the five sets of boundary conditions derived in the paper, three are already known, but only for domains with a trivial topological structure, while the remaining two are new. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献