✦ LIBER ✦
On finite difference potentials and their applications in a discrete function theory
✍ Scribed by K. Gürlebeck; A. Hommel
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 130 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.389
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We present a potential theoretical method which is based on the approximation of the boundary value problem by a finite difference problem on a uniform lattice. At first the discrete fundamental solution of the Laplace equation is studied and the theory of difference potentials is described. In the second part we define a discrete Cauchy integral operator and a Teodorescu transform. In addition a Borel–Pompeiu formula can be formulated. Copyright © 2002 John Wiley & Sons, Ltd.