This paper obtains the Cauchy-Pompeiu formula on certain distinguished boundary for functions with values in a universal Clifford algebra. This formula is just an extension of the Cauchy's integral formula obtaine...This paper obtains the Cauchy-Pompeiu formula on certain distinguished boundary for functions with values in a universal Clifford algebra. This formula is just an extension of the Cauchy's integral formula obtained in [11].展开更多
By using the solution to the Helmholtz equation u-λu = 0(λ≥ 0),the explicit forms of the so-called kernel functions and the higher order kernel functions are given.Then by the generalized Stokes formula,the integra...By using the solution to the Helmholtz equation u-λu = 0(λ≥ 0),the explicit forms of the so-called kernel functions and the higher order kernel functions are given.Then by the generalized Stokes formula,the integral representation formulas related with the Helmholtz operator for functions with values in C(V3,3) are obtained.As application of the integral representations,the maximum modulus theorem for function u which satisfies Hu = 0 is given.展开更多
基金Project supported by RFDP of Higher Education and NNSF of China, SF of Wuhan University.
文摘This paper obtains the Cauchy-Pompeiu formula on certain distinguished boundary for functions with values in a universal Clifford algebra. This formula is just an extension of the Cauchy's integral formula obtained in [11].
基金Project supported by Deutscher Akademischer Austausch Dienst (German Academic Exchange Service)the National Natural Science Foundation of China (No.10471107)
文摘By using the solution to the Helmholtz equation u-λu = 0(λ≥ 0),the explicit forms of the so-called kernel functions and the higher order kernel functions are given.Then by the generalized Stokes formula,the integral representation formulas related with the Helmholtz operator for functions with values in C(V3,3) are obtained.As application of the integral representations,the maximum modulus theorem for function u which satisfies Hu = 0 is given.
