  We study the solvability of singular Abreu equations which arise in the
approximation of convex functionals subject to a convexity constraint. Previous
works established the solvability of their second boundary value problems
either in two dimensions, or in higher dimensions under either a smallness
condition or a radial symmetry condition. Here, we solve the higher dimensional
case by transforming singular Abreu equations into linearized Monge-Amp\`ere
equations with drifts. We establish global H\"older estimates for the
linearized Monge-Amp\`ere equation with drifts under suitable hypotheses, and
then use them to the regularity and solvability of the second boundary value
problem for singular Abreu equations in higher dimensions. Many cases with
general right-hand side will also be discussed.
