Riquier and Dirichlet boundary value problems for slice Dirac operators
Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 149-163
Published online January 31, 2018
Hongfen Yuan
Hebei University of Engineering
Abstract : In recent years, the study of slice Dirac operators has attracted more and more attention in the literature. In this paper, Almansi-type decompositions for null solutions to the iterated slice Dirac operator and the generalized slice Dirac operator are obtained without a star-like domain centered at the origin. As applications, we investigate Riquier type problems and Dirichlet type problems in the theory of slice monogenic functions.
Keywords : slice Dirac operator, Euler operator, generalized slice Dirac operator, Riquier problem, Dirichlet problem
MSC numbers : 30G35, 30E25, 35G15
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