On singular Abreu equations in higher dimensions

Abstract

We study the solvability of the second boundary value problem of a class of highly singular, fully nonlinear fourth order equations of Abreu type in higher dimensions under either a smallness condition or radial symmetry.

v2: modified a bit the statement and the proof of Proposition 1.7; v3: strengthened and simplified the proof of Theorem 1.3; This note is a sequel to arXiv:1811.02355