(x)dx-\int_{\Omega}v(x)[\Delta u(x)-\lambda u(x)]dx\\ 前一项为boundary term,假设为0,略去,第二项,对于任意的v(x),均满足等式恒为0,则 \Delta u(x)-\lambda u(x)\equiv0 .即 \Delta u(x)=\lambda u(x) ,可见拉格朗日乘子 \lambda 为laplacian算子的特征值, u(x) 是其特征函数...
Twitter Google Share on Facebook Laplace operator (redirected fromLaplacian operator) Encyclopedia n (Mathematics)mathsthe operator ∂2/∂x2+ ∂2/∂y2+ ∂2/∂z2,. Symbol:∇2Also called:Laplacian Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins...
The form Boundedness criterion for the Laplacian operator - Gala () Citation Context ...trix field such that H ∈ BMO ( R d) d 2 . AMS Mathematics Subject Classification (2000): 42B20, 42B35 Key words and phrases: Sobolev spaces, distribution, BMO spaces 1. Introduction Recently, S. ...
Another option is to turn it into a multiple of the square of the Laplace operator. Get syms d Laplace = @(u) laplacian(u,[x,y]); expand(d*Laplace(Laplace(u))) ans(x, y) = d ∂4∂x4 u(x,y)+2 d ∂2∂y2 ∂2∂x2 u(x,y)+d ∂4∂y4 u(x,...
2. If the grid cells are square (that is, ifdx =y, which we assume for the remainder of this chapter), the Laplacian simplifies to: Equation 3 The Laplacian operator appears commonly in physics, most notably in the form of diffusion equations, such as the heat equation. Equation...
Truncation errors of four stencils for evaluating the two-dimensional Laplacian operator are discussed, and response functions are computed. The efficiencies of the stencils, in terms of number of iterations and computer time required, f... HR Glahn - 《Journal of Atmospheric Sciences》 被引量: ...
Two generalized finite difference representations of the n -dimensional Laplacian operator are obtained vectorialiy by extensions of the techniques previously developed for three-dimensional space. Each representation is presented in a form which can readily be applied at the nodes generated in an automa...
We prove a two-term asymptotic expansion of eigenvalue sums of the Laplacian on a bounded domain with Neumann, or more generally, Robin boundary conditions. We formulate and prove the asymptotics in terms of semi-classical analysis. In this reformulation it is natural to allow the function descr...
定义3.1 拉普拉斯二次型 Laplacian quadratic form ***例子3.2 ***例子3.3 定理3.4(求 ) 3.2 极大连通子图/连通分量的数量 Counting connected components 3.2.1 The oriented incidence matrix 定向关联矩阵 定义3.5 例子3.6 定理3.7 定向关联矩阵的秩 定理3.8 定向关联矩阵和拉普拉斯矩阵的关系 例子3.9 推论3.10 ...
Thieullen, Eigenfunctions of the Laplacian and asso- ciated Ruelle operator, Nonlinearity, Volume 21, Number 10, 2239-2254 (2008)A. Lopes and P. Thieullen, Eigenfunctions of the Laplacian and associated Ruelle operator, Nonlinearity, Volume 21, Number 10, 2239-2254 (2008)...