for any functions in $C_2^2$, we have a $-D^2$ operator $-D^2u=-(u_{xx}+u_{yy})$
However now i need to transform this operator from $(x,y)$ to $(r,\theta)$ for some sphere boundary condition, how am I suppose to do? As we know that $x=r\cos\theta,y=r\sin\theta$.
the form should be something near $-(u_{\theta\theta}+u_{rr})$