Cauchy type integrals and a boundary value problem in a complex Clifford analysis

Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its conclusions can be applied to the Maxwell equation, Yang-Mill field theory, quantum mechanics and value problems. In this paper, we first give the definition o...

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Bibliographic Details
Published in:Acta mathematica scientia 2024, Vol.44 (1), p.369-385
Main Authors: Cao, Nanbin, Li, Zunfeng, Yang, Heju, Qiao, Yuying
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:Clifford analysis is an important branch of modern analysis; it has a very important theoretical significance and application value, and its conclusions can be applied to the Maxwell equation, Yang-Mill field theory, quantum mechanics and value problems. In this paper, we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis, and get the Plemelj formula for it. Second, we discuss the Hölder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra. Finally, we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-024-0120-4