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

doi:10.1016/S0252-9602(12)60158-1

Abstract

Abstract:

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

CLC Number:

30G35

JIANG Le, DU Jin-Yuan. RIEMANN BOUNDARY VALUE PROBLEMS FOR SOME K-REGULAR FUNCTIONS IN CLIFFORD ANALYSIS[J].Acta mathematica scientia,Series B, 2012, 32(5): 2029-2049.

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