0
$\begingroup$

How can we show that a Dirichlet problem for Laplace's equation in a finite region has a unique solution.

Usually we can consider u2 - u1, a difference in values.

  • 0
    Can you use the maximum principle?2012-11-01

1 Answers 1

2

If $u_1$ and $u_2$ solve Laplace's equation on the same domain with the same boundary conditions, then $u_2 - u_1$ solves Laplace's equation with $0$ boundary conditions. The maximum principle now implies that $u_2 - u_1 = 0$.

  • 0
    Unfortunately, I'm not so sure if we can use the MaxPrinciple. Can you illustrate with another attempt? Thanks2012-11-01