## Mathematical Sciences Faculty Publications

#### Title

A variant of Hörmander's L 2 existence theorem for the Dirac operator in Clifford analysis

Article

2014

#### Publication Source

Journal of Mathematical Analysis and Applications

410

no. 1

39-54

#### DOI

10.1016/j.jmaa.2013.08.005

0022-247X

#### Abstract

In this paper, we give the H\"ormander's L2 theorem for Dirac operator over an open subset $\Omega\in\R^{n+1}$ with Clifford algebra. Some sufficient condition on the existence of the weak solutions for Dirac operator has been found in the sense of Clifford analysis. In particular, if Ω is bounded, then we prove that for any f in L2 space with value in Clifford algebra, there exists a weak solution of Dirac operator such that D¯u=f

with u in the L2 space as well. The method is based on H\"ormander's L2 existence theorem in complex analysis and the L2 weighted space is utilised.

#### Disciplines

Mathematics

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