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

作者：Liu, Yang^*; Chen, Zhihua; Pan, Yifei

来源：Journal of Mathematical Analysis and Applications, 2014, 410(1): 39-54.

DOI：10.1016/j.jmaa.2013.08.005

• Hormander's L-2 theorem
• Clifford analysis
• Weak solution
• Dirac operator

In this paper, we give the Hormander's L-2 theorem for the Dirac operator over an open subset Omega is an element of Rn+1 with Clifford algebra. Some sufficient condition on the existence of the weak solutions for the Dirac operator has been obtained in the sense of Clifford analysis. In particular, if Omega is bounded, then we prove that for any f in L-2 space with value in Clifford algebra, there exists a weak solution of the Dirac operator such that
(D) over baru = f
with u in the L-2 space as well. The method is based on Hormander's L-2 existence theorem in complex analysis and the L-2 weighted space is utilized.

• 出版日期2014-2-1
• 单位江西师范大学; 同济大学; 浙江师范大学