Solvability of singular Abreu equations in higher dimensions
ABSTRACT
Singular Abreu equation is a system of two equations, where one of them is a Monge–Ampère equation and the other is a linearized Monge–Ampère equation. They are used in the approximation of minimizers to variational problems with 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. In this talk, we discuss methods that can be used to show the solvability of singular Abreu equation in dimensions higher than 2.
This is based on a joint work with Nam Q. Le (Indiana University), Ling Wang (Bocconi Universiy), and Bin Zhou (Peking University).
This talk will be delivered in Korean.
