先验估计

Sturm-Liouville问题先验估计的改进

Improvements on the Prior Estimate of Sturm-Liouville Problem

利用Sobolev插值不等式以及关于时间t的先验估计证明了该方程在无界域上解的存在性；

The Sobolev interpolation inequality and prior estimate on time are applied to show the existence of solution in unbounded domain .

提出一种全新的基于空间滤波理论的正则化方法，它不依赖于阻抗分布的先验估计，因此它比最大后验（MAP）正则化方法易于实现；

We developed a new regularization method based on the spatial filtering theory , which is independent on the estimation of impedance distribution .

基于先验估计的自适应Chirplet信号展开

Adaptive Chirplet Signal Expansion Based on Transcendental Estimation

并且利用微分方程先验估计的理论和技巧，得到了严谨的L2模误差估计。

The optimal order estimates in L2 - norm of the procedure are obtained respectively by using the theory and techniques of priori estimate of differential equations .

应用变分方法，综合利用先验估计，含测度的方程，该文通过求解一个具有非凸约束的局部极小化问题，得到所考虑的Plateau问题的有界解之存在性。

This paper proved the existence of bounded solutions for this kind Plateau problem by solving a local minimizing problem with nonconvex constraint via the calculus of variation , equation with measures and prior estimates .

应用向量积计算及先验估计理论和技巧，得到最佳的L2误差估计。

Using the calculation of the vecter product , and the theory and technique of prior estimates , then the optimal order error estimates in L2 are obtained .

研究了一类广义长短波（LS）方程柯西问题的整体解，利用对时间的一致先验估计方法，证明了整体解的存在性、惟一性。

Applying the integral a priori estimates method , the existence and uniqueness of the global solution for the system of the interaction of generalized long wave and short wave are proved .

我们将能量Casimir方法与现代非线性偏微分方程理论中的非线性先验估计方法有创新性地结合起来，在该领域取得了突出的成果。

The author and his research group have combined the Energy Casimir method with the a prior estimate method innovatively and have attained outstanding achievements .

通过解的先验估计研究Banach空间中Sturm-Liouville两点边值问题的非平凡解的存在性，改进和推广了已有结果。

This paper establishes the existence of nontrivial solutions of Sturm-Liouville two point boundary value problems in Banach spaces by the prior estimate of solutions . This extends known results .

运用有限差分法与精细的先验估计，对具有Gilbert阻尼的Heisenberg自旋链系统进行了研究。

To accomplish , the authors first study the system of the Heisenberg spin chain with Gilbert damping by applying the finite difference technics and the delicate a priori estimations .

利用微分方程的先验估计理论和技巧，分别得到了椭圆型方程和抛物型方程的最优H1和L2误差估计。

Using the theory and technique of a priori estimate of differential equation , the author obtains the optimal order error estimates in H1-norm and L2-norm of the elliptic equation and parabolic equations respectively .

第四，通过先验估计，证明了广义Sine-Gordon方程在齐次边界条件和初始条件下所确定的无穷维动力系统在各种Sobolev空间的有界吸收集的存在性。

By the priori estimates , we prove the existence of absorbing set of the Sine-Gordon function under initial and the first bound condition in different sobolev space .

本文利用Krylov关于非线性椭圆方程，非线性抛物方程的先验估计的思想方法，给出了一类非线性抛物方程边值问题的解的Holder模估计。

An estimate of Holder norm for solutions of a class of boundary value problems of nonlinear parabolic equations is given in this paper . The methods used here were first created by Krylov .

对凸体理论中的一类二阶完全非线性偏微分方程的正解给出了C1先验估计。

The authors in this paper get a C ~ 1 apriori estimate for the positive k-convex solutions of some fully nonlinear second order partial differential equation , which arises in the convex bodies theory .

通过引入权空间，应用内插不等式和先验估计，获得复Ginzburg-Landau方程整体弱吸引子的存在性。

By introducing the weighted space , and applying interpolation inequality and a prior estimate , the existence of weak global attractor of complex Ginzburg-Landau equations is obtained .

本文利用特征线的方法，得到关于拟线性双曲方程组Cauchy问题经典解的一致先验估计.这样的估计给出了系统经典解存在区间的下界。

This paper obtains a uniform a priori estimate of classical solution to the Cauchy problem for quasilinear hyperbolic system by using the method of characteristic , which gives a lower bound on life-span of the classical solution .

本文研究n阶方程组的非线性Riemann-Hilbert边值问题，建立该问题的解的表达式，并利用先验估计和Banach压缩映像原理证明解的存在性。

In this paper the representation formulae of the solution to nonlinear Riemann-Hilbert problem for a class of nth order systems are established , and the existence of the solution is proved by use of a priori estimation and Banach mapping theorem .

我们运用精确的先验估计得到了Hasegawa-Mima-Charney-Obukhov方程强解的整体存在性。

We use a priori estimates to get the global existence of strong solution for an Hasegawa-Mima-Charney-Obukhov equation .

文中讨论了三维Dirichlet问题的增量未知元方法的先验估计，这种估计是在三个坐标方向上的部分具有相同的非一致性的特殊情形下得到的。

The present paper studies a priori estimates of incremental unknowns methods for Dirichlet problems with space dimensions three . One gets the estimates on a class of special nonuniform meshes which are the same in the three coordinate directions .

先验估计依赖构造辅助函数，证明依靠截断技术、Leray-Schauder不动点定理和指数变换。

A-prior estimate is based on constructing an auxiliary function , and the proofs rely on the truncation technique , the Leray-Schauder fixed point theorem and an exponential variable transformation .

此文研究一类在Radon测度给定下二阶退化拟线性椭圆型方程.通过引入逼近子问题列并求解、先验估计和收敛性研究，证明了该方程广义解在带权Sobolev空间的存在性。

This paper deals with a quasilinear degenerate elliptic equation with Radon-measures as date . By introducing a sequence of approximating problems and their solution , studying priori estimate and convergence , we prove the existence of weak solution in a weighted sobolev space .

对一类反应扩散方程及方程组的初边值问题提出分数步长差分格式.利用高阶差分算子的分解，以及先验估计的理论和技巧，得到次优阶l2误差估计。

The factional step difference scheme is given for the initial boundary problem of a class of nonlinear reaction-diffusion equation and systems . Using the factor of high order difference operator and the theory and technique of prior estimates , suboptimal order error estimates in l2 is obtain .

本文建立了联系于Riemann边值条件的标准Beltrami方程的解的表示及先验估计。这些结果可能被用来证明非线性问题的解的存在性和唯一性。

A representation and a priori estimate for the solution of the canonical Beltrami equation in connection with Riemann boundary conditions are developed , which may be used for existence as well as uniqueness statements for related nonlinear problem .

运用关于时间的一致先验估计，证明了具有周期边值条件的广义Hasegawa-Mima方程整体解的存在性、惟一性。

Applying the integral a priori estimates method , the existence and uniqueness of the global solution for the generalized Hasegawa-Mima equation with initial periodic boundary condition was proved .

通过Bernstein方法，对来源于凸体几何中的Christoffel-Minkowski问题，建立了球面上的退化的Hessian方程的C（~1,1）先验估计，在一定程度上推广了Krylov的结果。

Based on Bernstein 's technique , this paper established the C ~ ( 1,1 ) a priori estimates for degenerate Hessian equation on S ~ n , which is corresponding to Christoffel-Minkowski problem in convexity geometry . It refined the results of Krylov .

研究了一类变系数自伴算子&Heisenberg群上的Kohn－Laplace算子多项式的特征值问题.利用Heisenberg群上的表示及其Fourier变换，获得了该特征值问题的特征值的一些先验估计。

The work is devoted to eigenvalue problems associated with a class of variable coefficients selfadjoint operators & Kohn Laplace operator on Heisenberg group . One obtains some priori estimate for discrete eigenvalues of the problem by group representation and Fourier transformation theory on n dimensional Heisenberg group .

首先利用压缩映象原理，结合一些先验估计式及Bessel函数的收敛性，根据KleinGordon方程初值问题的等价积分方程，在二次连续可微空间中得到了初值问题解的适定性；

Firstly , using the contraction mapping principle , combining some priori estimates and the convergence of Bessel function , the well_posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein_Gordon equations .

在本章中，运用离散泛函分析理论，结合先验估计、Brouwer不动点原理证明了相应差分格式解的存在唯一性、收敛性和稳定性。

In this chapter , the existence and uniqueness of the solution to the scheme , the convergence and stability to the scheme are proved by using discrete functional analysis theory , the apriority estimate method and the Brouwer fixed-point theory .

对于两类具有一端点值固定的两种不同的边界条件来寻找不同的先验估计，获得了两类二阶三点边值问题解的存在性，并利用Leray-Schauder不动点定理建立解的存在定理。

By using different methods , we obtain the different prior estimates with their values fixed at one end point and different boundary conditions . Thus , we establish the existence theorems of solutions by employing Leray-Schauder fixed theorem .