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Half Dirichlet problems for powers of the Dirac operator in the unit ball of \(\mathbb R^m\) \((m\geq 3)\). (English) Zbl 0729.35040

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.

MSC:

35Q40 PDEs in connection with quantum mechanics
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35C15 Integral representations of solutions to PDEs
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