Yes lambda, mu, J2 etc are constants.
the circled triple integral means is not important. It shows integral on the volume.
V indicates that integral is taken on the volume.
the change of variables is used for simplification only and it is not an important issue.
the quantities Ji , miu, lambda, omega, rho, A,B,C are constants.
the assumption (4) is used and then substituting in the Eq. 1, but you consider only Eq
7 as a final equation and take differential with respect to the constants A,B,C.
Aijk and Bijk and Cijk are unique? Are
but Jijk for example is a function.see Eq. 4. They are functions of (sigma, theta, phi) and are differentiable.
Please see pages 2 and 3 of attached file.
Tnanks so much for your attention and your help.