laplacià

d_{xx}^{2}[u(x,y,z)]+d_{yy}^{2}[u(x,y,z)]+d_{zz}^{2}[u(x,y,z)] = k

u(x,y,z) = (k/6)·x^{2}+(k/6)·y^{2}+(k/6)·z^{2}

d_{xx}^{2}[u(x,y,z)]+d_{yy}^{2}[u(x,y,z)]+d_{zz}^{2}[u(x,y,z)] = k·xyz

u(x,y,z) = (k/18)·x^{3}yz+(k/18)·y^{3}zx+(k/18)·z^{3}xy

d_{xx}^{2}[u(x,y,z)]+d_{yy}^{2}[u(x,y,z)]+d_{zz}^{2}[u(x,y,z)] = k·( x+y+z )

u(x,y,z) = (k/6)·x^{3}+(k/6)·y^{3}+(k/6)·z^{3}

d_{xx}^{2}[u(x,y,z)]+d_{yy}^{2}[u(x,y,z)]+d_{zz}^{2}[u(x,y,z)] = k·( xyz )^{2}

u(x,y,z) = ...

... (k/36)·x^{4}y^{2}z^{2}+...

... (-1)·(k/36)·x^{4}·(1/12)·z^{4}+(-1)·(k/36)·x^{4}·(1/12)·y^{4}+...

... (k/36)·x^{2}·(1/30)·z^{6}+(k/36)·x^{2}·(1/30)·y^{6}+...

... (-1)·(k/36)·(1/15)·(1/56)·z^{8}+(-1)·(k/36)·(1/15)·(1/56)·y^{8}+...