Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Eigenfunctions of the Laplace operator

The study of the Laplace operator and its corresponding eigenvalue problem is crucial to understand the foundations of 3D shape analysis. For that reason the most important mathematical properties of the Laplace operator in Euclidean spaces, its eigenvalues and eigenfunctions are summarized and explained in this report. The basic definitions and concepts of infinite dimensional function spaces,...

متن کامل

Asymptotic Property of Eigenvalues and Eigenfunctions of the Laplace Operator in Domain with a Perturbed Boundary

In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We derive recursive formulas for the Taylor coefficients of the eigenvalues as functions of the shape-perturbation parameter and we establish the existence of a set of eigenfunctions that is ...

متن کامل

Eigenvalues of the Laplace Operator on Certain Manifolds.

To every compact Riemannian manifold M there corresponds the sequence 0 = X1 < X2 < X3 .< ... of eigenvalues for the Laplace operator on M. It is not known just how much information about M can be extracted from this sequence.' This note will show that the sequence does not characterize M completely, by exhibiting two 16-dimensional toruses which are distinct as Riemannian manifolds but have th...

متن کامل

Eigenvalues Estimates for the p-Laplace Operator on Manifolds

The Laplace-Beltrami operator on a Riemannian manifold, its spectral theory and the relations between its first eigenvalue and the geometrical data of the manifold, such as curvatures, diameter, injectivity radius, volume, has been extensively studied in the recent mathematical literature. In the last few years, another operator, called p-Laplacian, arising from problems on Non-Newtonian Fluids...

متن کامل

Eigenvalues of the fractional Laplace operator in the unit ball

We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (−∆)α/2 in the unit ball D ⊂ Rd, with a Dirichlet condition in the complement of D. The standard Rayleigh–Ritz variational method is used for the upper bounds, while the lower bounds involve the less-known Aronszajn method of intermediate problems. Both require exp...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Applications of Mathematics

سال: 1998

ISSN: 0862-7940,1572-9109

DOI: 10.1023/a:1023269922178