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Nonlinear Analysis

Solutions to the Monge-Ampere equation with polyhedral and Y-shaped singularities

Connor Mooney, UC Irvine

Location:  Zoom
Date & time: Wednesday, 13 October 2021 at 9:30AM - 10:30AM

Abstract: The Monge-Ampere equation det(D^2u) = 1 arises in prescribed curvature problems and in optimal transport. An interesting feature of the equation is that it admits singular solutions. We will discuss new examples of convex functions on R^n that solve the Monge-Ampere equation away from finitely many points, but contain polyhedral and Y-shaped singular structures. Along the way we will discuss geometric and applied motivations for constructing such examples, as well as their connection to a certain obstacle problem.

Zoom link
Meeting ID: 964 3090 5091 Passcode: 491508