Special Session 82: Recent Advances in Nonlinear PDEs and Free Boundary Problems

Free boundaries and the minimal surface system

Connor Mooney

USA
Co-Author(s):    
Abstract:
We will discuss two free boundary problems that arise in the study of minimal surfaces of high codimension. The first one shows that viscosity solutions to the special Lagrangian equation need not be $C^1$, or have minimal gradient graph. The second one shows that large interior singularities can arise when minimizing area among graphs in codimension two or larger. This is joint work with O. Savin.