Abstract
By using the solution to the Helmholtz equation Δu − 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.
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