On a Dirichlet problem for a generalized Beltrami equation (Q1668595)

Let $\Omega\subset \mathbb{R}^{n+1}$ be a domain with sufficiently smooth boundary $\Gamma=\partial\Omega$. Consider functions $f$ in $\Omega$ with values in the Clifford algebra over $\mathbb{R}^n$ with the usual basis and multiplication rules. Conditions are given whereby the Dirichlet problem \[\begin{split}Du=q\bar{D} w\quad &\text{in }\Omega\quad(q\text{ is a smooth function}),\\ w= g\quad &\text{on }\Gamma= \partial\Omega,\end{split}\] is uniquely solved in some spaces and a representation formula for the solution is obtained. Used in the study is [\textit{K. Gürlebeck} and \textit{U. Kähler}, Z. Anal. Anwend. 15, No. 2, 283--297 (1996; Zbl 0864.30039)].