In this paper, we find some superharmonic functions, which relate to the convexity estimates for Green's function and the first eigenfunction of Laplace operator with homogeneous Dirichlet boundary conditions in bounded convex domains of R-n.Jia, Xiaohan...
英['aɪgənfʌŋkʃən] 美['aɪgənfʌŋkʃən] 是什么意思 n. 特征函数; 英英释义 Eigenfunction vibrating drum problem is, at any point in time, an eigenfunction of the Laplace operator on a disk.]] 以上来源于:Wikipedia ...
Laplace Operator wavefunction ψ Eigenvalue Problem View all Topics Recommended publications Journal of Differential Equations Journal Journal of Mathematical Analysis and Applications Journal Applied Mathematics and Computation Journal Journal of Computational and Applied Mathematics JournalBrowse books and journal...
Find the five smallest eigenvalues and eigenfunctions of a Laplace equation on a square torus with a Dirichlet constraint. 在狄利克雷约束下求拉普拉斯方程在一个矩形环面上最小的五个周期特征值和特征函数. ParaCrawl Corpus \[ScriptCapitalB] = DirichletCondition[u[x, y] == 0, True]; Compute ...
Let(M,g)be a compact Riemannian surface. Consider a family ofL2normalized Laplace–Beltrami eigenfunctions, written in the semiclassical form−hj2Δgφhj=φhj, whose eigenvalues satisfyhhj−1∈(1,1+hD]forD>0a large enough constant. LetPhbe a uniform probability measure on theL2unit-sphereS...
WefirstrecallthattheassociatedLaplace-Beltramioperator∆=∆ g ,haseigenvalues {−λ 2 ν },where0≤λ 2 0 ≤λ 2 1 ≤λ 2 2 ≤...arecountedwithmultiplicity.Let{φ ν (x)}bean associatedorthonormalbasisofL 2 -normalizedeigenfunctions.Ifλ 2 isinthespectrumof −∆,letV λ ={φ:...
In this paper, we find some superharmonic functions, which relate to the convexity estimates for Green's function and the first eigenfunction of Laplace operator with homogeneous Dirichlet boundary conditions in bounded convex domains of R n ....
Mandible shape modeling using the second eigenfunction of the Laplace-Beltrami operator. In: Proceedings of SPIE Medical Imaging, p. 79620Z.Seo, S., Chung, M.K., Whyms, B.J. and Vorperian, H.K. (2011) Mandible Shape Modeling Using the Second Eigenfunction of the Laplace-Beltrami ...
We describe the spectral projection of the LaplaceBeltrami operator in n-dimensional hyperbolic space by studying its resolvent as an analytic operator-valued function and applying the technique of contour integration. As a result an integral formula is established for the associated Legendre function...
Finally, we uncover a new divergence phenomenon for eigenfunction expansions of characteristic functions of balls, for a perturbation of the Laplace operator on a sphere of dimension 鈮 5.doi:10.1081/PDE-120002866TaylorMichael E.Marcel Dekker, Inc.Communications in Partial Differential Equations...