Complex Clifford-analysis and elliptic boundary value problems
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 \(q\).
complex Clifford algebra \({\mathcal C}\ell\)
scientific article; zbMATH DE number 861897