Question

Which one of the following is a property of the solutions to th Laplace equation; ${▽}^{2}f=0$?

• A. The solutions have neither maxima nor minima anywhere except at the boundaries
• B. The solution are not separable in the coordinates
• C. The solutions are not continuous
• D. The solutions are not dependent on the boundary conditions.

Answer 1

The correct option is A The solutions have neither maxima nor minima anywhere except at the boundaries

Laplace equation; ${▽}^{2}f=0$ can be used in any of the three co-ordinate system and its solutions are continuous. Moreover, the constants that occur while solving ${▽}^{2}f=0$ can be found only using boundary conditions.
So the solutions have neither maxima nor minima anywhere except at the boundaries