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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 [tex]V(x,y)[/tex] is harmonic because of the above.

Does it means that [tex]\nabla ^2V[/tex] is consequently equal to zero ?

How would V behave if

[tex]\nabla ^2V>0[/tex]

and

[tex]\nabla ^2V<0[/tex]

?

thanku