实Clifford分析中的一个边值问题

A BOUNDARY VALUE PROBLEM IN THE REAL CLIFFORD ANALYSIS

考虑以 e_A=e_(α1)…e_(αh)(A={α_1,α_2,…,α_h)(?){1,2,3,…,n),1≤α_1<α_2<…<α_h≤n)为基底元素的实 Clifford 代数 A_n(R),其中 e_1=1,e_k^2=-1(k=2,3,4,…,n),e_ke_m+e_me_k=0(k≠m,k,m=2,3,4,…,n).并用 V_n 表示由向量组 e_1,e_2,…,e_n 所张成的 A_n(R)的子空间,V_n 中元素为 x=(?)x_ke_k,A_n(R)

In papars [1] and [17],the authors have studied the boundary value problems for the reg-ular functions in the Clifford analysis.In this paper,by using Hua Luogeng's results,the author proves the solvability theorem of a boundary value problem for a second order par-tial differential equation in the Clifford analysis in he unit hyperball,and gives the integralrepresentation of solution for this problem.