Liquid Crystal - Director distribution

Hello,

I would like to calculate the director distribution of liquid crystals.

The formula

fs=1/2(K11*(div n)^2 + K22*(n * rot n + q0)^2 +K33* |(n x rot n)|^2)

describes the Oseen-Frank free energy density for nemantic crystals.

K11, K22, K33 and q0 are constants. n are unit vectors presenting each director. (n is a vector with nx, ny and nz as elements).

At at least one boundary the director has known value (nx and ny are known).

A second energy density comes from the electric field:

fe=div grad(phi),

where phi is the electric potential.

The potential is given at the boundarys, at least at two edges:

------------------------------ +phi
LC
------------------------------ -phi

The energy has to be minimized:
Fs-Fe -->0

I think I have to use mathematical euqtions --> PDE in Comsol, but I do not know how to fill the template(s).

I have 2/3 variables, if I try to solve a 2D problem:

phi --> scalar at every grid point
n --> vector consiting of two scalars nx and ny

fs and fe are scalar fields.

Is it possible to compute the solution with Comsol and one of the PDE forms? Or do I need a weak form?
How can I fill in the PDE templates for this special task?

I thought about setting one energy as source term, but during my tries I got the problem, that n is a vector and fs, fe are just scalars.

Thanks a lot for any help.

Irina