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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Science, Hebei GEO University, Shijiazhuang, 050031, China

    Nanbin Cao

  2. College of Science, Hebei University of Science and Technology, Shijiazhuang, 050018, China

    Zunfeng Li & Heju Yang

  3. School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, 050024, China

    Yuying Qiao

Authors
  1. Nanbin Cao
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  2. Zunfeng Li
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  3. Heju Yang
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  4. Yuying Qiao
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Corresponding author

Correspondence to Zunfeng Li.

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Conflict of Interest The authors declare no conflict of interest.

Additional information

This work was supported by the NSF of Hebei Province (A2022208007), the NSF of China (11571089, 11871191), the NSF of Henan Province (222300420397).

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Cao, N., Li, Z., Yang, H. et al. Cauchy type integrals and a boundary value problem in a complex Clifford analysis. Acta Math Sci 44, 369–385 (2024). https://doi.org/10.1007/s10473-024-0120-4

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  • DOI: https://doi.org/10.1007/s10473-024-0120-4

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