Approximation of variational problems with convexity and twisted Harnack inequality

In this talk, we explain how to use singular fourth-order Abreu equations (which arise in complex geometry) to approximate minimizers of several variational problems with a convexity constraint (which arise in economics, elasticity, and physics). We will discuss a new tool that makes the analysis possible: a Harnack inequality for singular elliptic equations that satisfy certain twisted structures.

学术海报.pdf