Displaying 641 – 660 of 2162

Showing per page

On multi-parameter error expansions in finite difference methods for linear Dirichlet problems

Ta Van Dinh (1987)

Aplikace matematiky

The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an n -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an ( n -dimensional) rectangular grid in the directions of the individual...

On Neumann boundary value problems for elliptic equations

Dimitrios A. Kandilakis (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We provide two existence results for the nonlinear Neumann problem ⎧-div(a(x)∇u(x)) = f(x,u) in Ω ⎨ ⎩∂u/∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in N , a is a weight function and f a nonlinear perturbation. Our approach is variational in character.

On Neumann elliptic problems with discontinuous nonlinearities

Nikolaos Halidias (2001)

Archivum Mathematicum

In this paper we study a class of nonlinear Neumann elliptic problems with discontinuous nonlinearities. We examine elliptic problems with multivalued boundary conditions involving the subdifferential of a locally Lipschitz function in the sense of Clarke.

On nodal sets and nodal domains on S 2 and 2

Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili (2007)

Annales de l’institut Fourier

We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S 2 . We also construct a solution of the equation Δ u = u in 2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

Currently displaying 641 – 660 of 2162