Delanghe, R.; Sommen, F.; Xu, Zhenyuan Half Dirichlet problems for powers of the Dirac operator in the unit ball of \(\mathbb R^m\) \((m\geq 3)\). (English) Zbl 0729.35040 Bull. Soc. Math. Belg., Sér. B 42, No. 3, 409-429 (1990). Dirichlet-type problems for the Dirac operator \(D=\sum^m_{j=1}e_j\partial /\partial x_j\) in the unit ball of the Euclidean space \(\mathbb R^m\) \((m\geq 3)\), and also for its powers \(D^k\) \((k\geq 1)\), are considered. For \(k=1\), in some sense, the boundary value problem under consideration may be looked upon as seeing a “half Dirichlet problem”, as \(D^2=-\Delta\). The solution in an appropriate class of function is found and uniqueness is proved. Reviewer: I.J.Dorfman (Moskva) Cited in 1 ReviewCited in 1 Document MSC: 35Q40 PDEs in connection with quantum mechanics 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35C15 Integral representations of solutions to PDEs Keywords:existence; Dirac operator; half Dirichlet problem; uniqueness PDFBibTeX XMLCite \textit{R. Delanghe} et al., Bull. Soc. Math. Belg., Sér. B 42, No. 3, 409--429 (1990; Zbl 0729.35040)