Suppose is a region of and is the boundary of . Further suppose is a function , and suppose corresponds to taking a derivative in a direction normal to the boundary at any point. Then the Neumann problem is to find a function such that
Here represents the Laplacian operator and the second condition is that be a harmonic function on . The condition for the existence of a solution of the Neumann problem is that integral of the normal derivative of the function , calculated over the entire boundary , vanish. This follows from the identic equation
and from the fact that .
|Date of creation||2013-03-22 15:19:59|
|Last modified on||2013-03-22 15:19:59|
|Last modified by||dczammit (9747)|