Boundary value problems for powers of the Dirac operator. (English) Zbl 1211.30058
Summary: In this article, half Robin problems for powers of Dirac operator in the unit ball \(B\) of \(\mathbb R^m\) \((m\geq 3)\) are investigated. By using a certain kind of decomposition of k-monogenic functions an explicit formula for the solution and the necessary and sufficient conditions for the solvability of the problems are obtained.
MSC:
30G35 | Functions of hypercomplex variables and generalized variables |
35G05 | Linear higher-order PDEs |
35G15 | Boundary value problems for linear higher-order PDEs |
References:
[1] | Brackx F, Clifford Analysis (1982) |
[2] | Xu Z, Simon Stevin 64 pp 187– (1990) |
[3] | Abreu-Blaya R, Advances in Applied Clifford Algebras 11 pp 15– (2001) · Zbl 1061.30033 · doi:10.1007/BF03042036 |
[4] | Gong Y, Rn (m2), Complex Variables and Theory and Applications 49 pp 303– (2004) |
[5] | Delanghe R, Bulletin Mathématiques de la Société Mathématique de Belgique 42 pp 409– (1990) |
[6] | Xu Z, Advances in Analysis (2005) |
[7] | Cnops J, PhD-thesis (1989) |
[8] | Ryan J, Rafal Ablamowicz Lectures on Clifford (Geometric) Algebras and Applications (2003) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.