This coordinate system is -separable for the 3-variable Laplace equation.

There is considerable overlap between potential theory and the theory of the Laplace equation.

Although it is not a symmetry in the usual sense of the term, we can start with the observation that the Laplace equation is linear.

The Laplace equation has the convenient property that its solution is a sum over the contribution from each electrode.

The correct equation (part of the Laplace equations) is:

The real and imaginary parts of a complex analytic function both satisfy the Laplace equation.

A similar calculation shows that v also satisfies the Laplace equation.

Where high frequency currents are considered, with skin effect, the surface current densities and magnetic field may be obtained by solving the Laplace equation.

The particular solutions of the total Laplace equation are regular solid harmonics:

The Laplace tidal equations are still in use today.