## EVENT DETAILS AND ABSTRACT

**Analysis Seminar**
**Title:** Interior regularity for a quadratic partial differential equation

**Speaker:** Ravi Shankar

**Speaker Info:** University of Washington

**Brief Description:**

**Special Note**:

**Abstract:**

The sigma-2 equation is the 2nd symmetric polynomial of eigenvalues of the matrix of second derivatives (Hessian). The sigma-1 equation (trace) is the Laplacian, and solutions are interior regular. In contrast, the sigma-3 equation for dimension 3 (determinant) is the Monge-Ampere equation; strictly convex solutions are regular, but otherwise there are singular solutions. We show interior regularity for sigma-2 solutions assuming semiconvexity. Unlike for the Laplacian, this equation is not uniformly elliptic, so we have to somehow exploit the quadratic structure and semiconvexity to obtain the regularity estimate.

**Date:** Monday, October 21, 2019

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Ben Weinkove

**Contact email:** weinkove@math.northwestern.edu

**Contact Phone:** 847-491-5580

Copyright © 1997-2024
Department of Mathematics, Northwestern University.