Speaker: 

Connor Mooney

Institution: 

UC Irvine

Time: 

Tuesday, March 12, 2019 - 3:00pm to 4:00pm

Location: 

RH 306

A classical problem in the calculus of variations is to determine the regularity of minimizers of \int F(grad u), where F is convex. When the graph of F contains a line segment, minimizers are no better than Lipschitz. On the other hand, when F is smooth and uniformly convex, minimizers are smooth. The intermediate case that F is strictly convex but its second derivatives degenerate on some bounded set arises in applications ranging from statistical mechanics to traffic congestion, but little is known about the minimizers in this case. We will discuss recent results that take steps in this direction.