On the solution of boundary value problems for harmonic functions on surfaces in \(E_{3}\) (Q2459777)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the solution of boundary value problems for harmonic functions on surfaces in \(E_{3}\) |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solution of boundary value problems for harmonic functions on surfaces in \(E_{3}\) |
scientific article |
Statements
On the solution of boundary value problems for harmonic functions on surfaces in \(E_{3}\) (English)
0 references
8 November 2007
0 references
The equation \(\partial_i (a_{ij}\partial_j F)=0\) (\(i,j=1,2\)), which corresponds to a positive definite form \(a_{ij}dx_idx_j\), \(a_{ij}=a_{ji}\) is studied. It is proved that this equation is a Beltrami-Laplace equation on some surface in three-dimensional Euclidean space if and only if \(\det\| a_{ij}\| =1\).
0 references
Beltrami-Laplace equation
0 references
self-adjoint elliptic operator
0 references
