Neumann Problem

Neumann problem

[′nȯi‚män ‚präb·ləm]
(mathematics)
The determination of a harmonic function within a finite region of three-dimensional space enclosed by a closed surface when the normal derivatives of the function on the surface are specified.

Neumann Problem

 

(also the second boundary value problem of potential theory), a boundary value problem posed for second-order partial differential equations. In the simplest cases, particularly for the Laplace equation, the Neumann problem consists in finding in some region a solution of the equation having a given normal derivative on the boundary of the region. The problem was first systematically studied in 1877 by C. Neumann.

References in periodicals archive ?
His topics include the Kerzman-Stein operator and kernel,the Ahlfors map of a multiply connected domain, the classical Neumann problem, arc length quadrature domains, and Green's function and the Bergman kernel.
The approach was applied to solve Neumann problem and some mixed biharmonic problems on rectangle.
To the best of our knowledge, there is no analogous study for the Neumann problem.
They cover the Cauchy problem, the Dirichlet problem, the Neumann problem, the Neumann problem for a nonlocal nonlinear diffusion equation, nonlocal p-Laplacian evolution problems, the nonlocal total variation flow, and nonlocal models for sandpiles.
The Neumann problem is uniquely solvable in the weak sense if and only if for any z [not member of] [[bar.
By analogy with the Green function for the Dirichlet problem for a domain [OMEGA], we consider the Green type function for the Neumann problem for [OMEGA] (also known as Neumann's function, or Green's function for the Neumann problem or Green's function of the second kind).
The principal focus will be on what happens to the eigenstructure of the Neumann problem ([sigma] = 0) as [sigma] proceeds along rays emanating from the origin toward the point at infinity in the complex plane.
In Section 4, we describe the algorithms DRCHLT for the solution of the Dirichlet problem and NEUMAN for the Neumann problem.
For example, the three classical boundary value problems: the Dirichlet problem, the Neumann problem, and the mixed Dirichlet-Neumann problem can be reduced to (1.
In this paper we give necessary and sufficient conditions on the existence of global weak solutions to the Neumann problem (1.
If u is the (unique) harmonic solution of the Dirichlet- Neumann problem with boundary values of u equal to 0 on [[gamma].