Minimization of anisotropic energies in classes of rectifiable varifolds

We consider the minimization problem of an anisotropic energy in classes of drectifiable varifolds in Rn, closed under Lipschitz deformations and encoding a suitable notion of boundary. We prove that any minimizing sequence with density uniformly bounded from below converges (up to subsequences) to a d-rectifiable varifold. Moreover, the limiting varifold is integral, provided all the elements of the minimizing sequence are integral varifolds with uniformly locally bounded anisotropic first variation.