# On singular Abreu equations in higher dimensions

## TL;DR

This paper investigates the solvability of complex, highly singular fourth-order Abreu-type equations in higher dimensions, focusing on conditions like smallness or radial symmetry to establish solutions.

## Contribution

It introduces new solvability results for singular Abreu equations in higher dimensions under specific conditions, expanding understanding of these complex nonlinear PDEs.

## Key findings

- Solvability under smallness conditions
- Existence results with radial symmetry
- Extension of Abreu equations to 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.