# How to satisfy Laplace's equation ?

by hotel
Tags: equation, laplace, satisfy
 P: 12 Hi I am not quit sure I have understand the laplace equation correctly. I hope some one can help me with it. As far as I understand if we are able to differentiate any function twice, then the function is harmonic. so we assume $$V(x,y)$$ is harmonic because of the above. Does it means that $$\nabla ^2V$$ is consequently equal to zero ? How would V behave if $$\nabla ^2V>0$$ and $$\nabla ^2V<0$$ ? thanku
 Sci Advisor HW Helper P: 11,896 How to satisfy Laplace's equation ? One requirement is that the function be $C^{2}$ class on that domain.If that domain is open,you don't have any boundary conditions. Daniel.