多维重调和方程的基本解及有关边值问题

foundamental solution of multi-harmonic equation and correspondent boundary value problem

在广义函数的意义下 ,利用拉氏方程的基本解讨论了二维、三维双调和方程的基本解 ,并且进一步给出了n重调和方程的基本解的表达式 (n≥ 2 ) .最后通过引入格林函数给出方程Δ3Δ3u =f(x ,y ,z)

By means of generalised function,this paper discusses the fundamental solutions of double harmonic equation in 2 or 3 dimentions by using of Laplace equation's fundamental solutions,gives the expression of fundamental solution of n harmonic equation( n ≥2)and the integral expression of the solution of boundary value problem.for the equation Δ 3Δ 3 u=f(x,y,z) by introducing Green's function.