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.