Analysis Seminar | Nam Le (Indiana University)

Title: Singular Abreu equations and twisted Harnack inequality

Abstract: In this talk, we will briefly 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). Then we will talk about their solvability using a family of linearized Monge-Ampere equations with drifts. We will discuss a new tool that makes the analysis possible: a Harnack inequality for singular elliptic equations that satisfy certain twisted structures.

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