Analysis Seminar

Title: Interior regularity for a quadratic partial differential equation
Speaker: Ravi Shankar
Speaker Info: University of Washington
Brief Description:
Special Note:

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
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