A question about Green's theorem

[yang liu]

Hello.in this website：http://micromagnetics.org/micromagnetism/#mjx-eqn-eqaniso_uniaxial. I would like to know how to get (23) from the last term of (22) using Green's theorem? Because in Eq. (23), the integral element for the integration of the region Ωd is dr, i.e., the line integral. For boundary ∂ the integral element of the integration of Ωd is ds., i.e., the area fraction. But I think that the integral element of the integral of the region Ωd is ds, and the integral element of the integral of the boundary ∂ Ωd is dr. I'm confused about this, and my understanding may be wrong. In addition, Equation (23) cannot be derived using Green's theorem.

Thank you very much for your reply！I wish you all the best！

[Антон Луценко]

Hi, this forum is dedicated to mumax, not micromagnetism in general, and might not be the best place to get an answer to such question.