Yu Yuan, University of Washington
Title: Regularity for convex viscosity solutions to
special Lagrangian equations
Abstract: We present regularity for convex viscosity solutions
to the special Lagrangian equation. The "gradient" graphs of all
solutions are (Lagrangian) minimal surfaces in Euclidean space. In
contrast, there are Pogorelov-like singular (convex) solutions to the
Monge-Ampere equation, which is also the potential equation for
"gradient" graphs of scalar functions being maximal surfaces in
pseudo-Euclidean space.
This is joint work with Jingyi Chen and Ravi
Shankar.