How to specify a line integral on the boundary?

Hi there,

I am solving the GL equation on 2D, which contains the vector potential \mathbf{A} as a field.
In the equation there is a second derivative term \nabla\times\nabla\times\mathbf{A} .
After integration by parts, I get the a term like \int_{\partial\Omega} B(v_1, v_2)\cdot d\mathbf{s}, where B is the magnetic field, and v_1,v_2 are 2 test functions.

How do I incorporate this condition into the problem?
Thank you.