Title

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

Document Type

Article

Publication Date

2014

Publication Source

Journal of Mathematical Analysis and Applications

Volume

410

Issue

no. 1

Inclusive pages

39-54

DOI

10.1016/j.jmaa.2013.08.005

ISBN/ISSN

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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