数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 2029-2049.doi: 10.1016/S0252-9602(12)60158-1

• 论文 • 上一篇    下一篇

RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS

姜乐|杜金元   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2010-03-10 修回日期:2012-01-05 出版日期:2012-09-20 发布日期:2012-09-20
  • 基金资助:

    Supported by NSF of China (11171260) and RFDP of Higher Eduction of China (20100141110054).

RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS

 JIANG Le, DU Jin-Yuan   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2010-03-10 Revised:2012-01-05 Online:2012-09-20 Published:2012-09-20
  • Supported by:

    Supported by NSF of China (11171260) and RFDP of Higher Eduction of China (20100141110054).

摘要:

In this paper, we study the Rm (m > 0) Riemann boundary value prob-lems for regular functions, harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(Vn, n). By using Plemelj formula, we get the solutions of Rm (m > 0) Riemann boundary value problems for regular functions. Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions, we obtain the solutions of Rm (m > 0) Riemann boundary value problems for harmonic functions and bi-harmonic functions.

关键词: Riemann boundary value problem, harmonic function, bi-harmonic function, Plemelj formula

Abstract:

In this paper, we study the Rm (m > 0) Riemann boundary value prob-lems for regular functions, harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(Vn, n). By using Plemelj formula, we get the solutions of Rm (m > 0) Riemann boundary value problems for regular functions. Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions, we obtain the solutions of Rm (m > 0) Riemann boundary value problems for harmonic functions and bi-harmonic functions.

Key words: Riemann boundary value problem, harmonic function, bi-harmonic function, Plemelj formula

中图分类号: 

  • 30G35