Displaying similar documents to “Solving initial-boundary value problems for coupled systems of partial differential equations”

Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle

Milan Práger (1998)

Applications of Mathematics

Similarity:

A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.

Two-dimensional real symmetric spaces with maximal projection constant

Bruce Chalmers, Grzegorz Lewicki (2000)

Annales Polonici Mathematici

Similarity:

Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that λ ( V ) ≤ λ ( V n ) where V n is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that 4 / π = λ ( l ₂ ( 2 ) ) ≥ λ ( V ) for any two-dimensional real symmetric space V.