Complex Clifford-analysis and elliptic boundary value problems
type: Item
instance of: scholarly article
title: Complex Clifford-analysis and elliptic boundary value problems
zbMATH Open document ID: 0844.30031
author: K. Gürlebeck
author: F. Kippig
published in: Advances in Applied Clifford Algebras
publication date: 1996-09-05T00:00:00Z
review text: Let \(M\) be a compact, real, \(n\)-dimensional \(C^1\)-manifold in \(\mathbb{C}^n\), which together with its tangent spaces does not meet the null cones of its points. Over \(\mathbb{C}^n\) is defined the complex Clifford algebra \({\mathcal C}\ell\). Using a Borel-Pompeiu formula representation formulas for functions on \(M\) in a convenient Sobolev space are given. This leads to complete function systems in these Sobolev spaces and to an explicit solution in integral form of the following boundary value problem: \(-\sum^n_{j= 1} \partial^2 g/\partial z^2_j= f\) in \(M\) and \(g= q\) on \(M\), with some conditions for \(f\) and \(q\).
reviewed by: Klaus Habetha
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32V05
zbMATH DE Number: 861897
zbMATH Keywords: Clifford analysis
zbMATH Keywords: boundary value problems
zbMATH Keywords: Dirac operator
zbMATH Keywords: complex Clifford algebra \({\mathcal C}\ell\)
zbMATH Keywords: boundary value problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 861897