Question

Can anyone prove the uniqueness of solutions for the laplace equation?

Answer 1

I can't, personally, but the internet can!
http://www-solar.mcs.st-and.ac.uk/~andy/LectureNotes/Fundamentals1/node52.html

This proof involves a bit of vector calculus, which I presume you know...

Answer 2

Basically it's a proof by contradiction, assume that two different solutions exist and then show that their difference is zero on the entire domain (ie, that they are equal).

Answer 3

Thanks, I'll take a look through it

Answer 4

You really should ask these kinds of questions on the physics forum. Those people are much smarter.

Answer 5

Yea I post on physicsforms.com sometimes, they always know what they're doing, but usually takes longer