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